# Testing the size and speed of large continued fraction expansions of fractional powers of 2.  
# 27 jan 2005   (first revision up to 1670 finished 2 May 2005)
# 
# Note that the progam has two distinct types of output:
# first, we check the quantity of interest, namely, looking for large partial quotients (any partial quotient over 10^7),
# second, in order to verify that we are not exceeding our accuracy of 1200 digits, we need to verify that none of the denominators exceed 10^600, since the accuracy of the number to the fraction p/q is less than 1/q^2.  Thus, we print out any cases where the number of digits exceeds 570; plus any cases where the number of digits is small, less than 465.  
#  
> restart;
> with(numtheory):
Warning, the protected name order has been redefined and unprotected

> Digits:= 1200;
                         Digits := 1200
> 
> 
# 22554 seconds for one run with 2500 digits  so not realistic to extend to 2500 digits.
> for g from 2 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                      2, 1, 2, 382.7069160
                   58, 27, 5761, 574.5058187
                 181, 19, 21084841, 511.7957458
                181, 162, 42169682, 515.5603550
Warning,  computation interrupted
> g;
                              267
> for g from 267 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                 322, 29, 65087657, 522.6349813
                322, 293, 32543828, 524.5927404
                   346, 317, 542, 461.4633827
Warning,  computation interrupted
> g;
                              405
> for g from 405 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                   469, 1, 78290, 571.1337144
                 473, 460, 2401837, 574.6526550
                475, 124, 19764279, 517.1568710
                475, 351, 39528560, 503.4618736
                491, 321, 10290001, 494.3520608
                   523, 477, 640, 459.4050110
Warning,  computation interrupted
> g;
                              524
> for g from 524 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
Warning,  computation interrupted
> g;
                              588
> for g from 588 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                 599, 53, 10348329, 527.3285829
                 603, 82, 15439104, 534.0754788
                633, 301, 24727538, 515.3621877
                633, 332, 12363769, 539.1414310
                641, 211, 485058274, 521.3731508
Warning,  computation interrupted
> g;
                              641
> for g from 641 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                641, 211, 485058274, 521.3731508
                641, 430, 970116550, 519.8424035
                   643, 587, 458, 464.6647528
                 655, 36, 16751605, 532.3734071
                 681, 1, 97015756, 506.4483261
                681, 680, 48507878, 528.1417628
                  699, 275, 1381, 464.5457187
Warning,  computation interrupted
> g;
                              703
> for g from 703 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                   708, 655, 494, 462.0929299
                  711, 140, 10784, 573.1937252
                717, 406, 11534954, 541.1925426
                729, 350, 12438539, 523.8038310
                 761, 71, 12476525, 550.9033355
                  780, 109, 2631, 572.6206971
                 792, 5, 67911128, 513.5295080
                792, 787, 33955563, 515.9825809
Warning,  computation interrupted
> g;
                              810
> for g from 810 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                823, 540, 11884568, 514.3669403
                827, 127, 13347726, 536.0540667
                 834, 811, 244302, 571.4175706
Warning,  computation interrupted
> g;
                              858
> for g from 858 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                   881, 552, 251, 462.9204411
                883, 810, 10490840, 527.9443026
Warning,  computation interrupted
> g;
                              891
> 
> for g from 883 to 1670 do
> for r from 1 to g-1 do
> if gcd(g,r) = 1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 470 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                883, 810, 10490840, 527.9443026
                903, 557, 13115870, 495.8390964
                  904, 623, 1725, 461.7541889
                 905, 95, 21084841, 511.7957458
                905, 810, 42169682, 515.5603550
Warning,  computation interrupted
> g;
                              908
> for g from 908 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 470 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                925, 183, 15172763, 503.7717883
                925, 742, 30345528, 507.5640525
                  944, 703, 8673, 574.4761794
                  949, 472, 4471, 570.6057109
                969, 439, 21307532, 534.2431712
                969, 530, 42615064, 522.0730142
                973, 204, 11162364, 518.4390200
                977, 130, 37224565, 523.1554771
                977, 847, 74449132, 489.5912552
Warning,  computation interrupted
> g;
                              998
> for g from 998 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 470 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1003, 730, 14190583, 534.4684432
                  1004, 923, 508, 468.9869175
                  1023, 371, 454, 468.5745866
                  1025, 382, 921, 463.1078019
                  1025, 394, 1917, 466.4877108
                  1027, 687, 784, 469.7649821
Warning,  computation interrupted
> g;
                              1030
> for g from 1030 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1031, 348, 29312365, 523.4915277
                1031, 683, 14656182, 525.3439200
                  1031, 697, 972, 463.3159557
                1053, 304, 15889092, 503.4694307
Warning,  computation interrupted
> g;
                              1063
> for g from 1063 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                  1068, 481, 2350, 570.9303322
                1081, 950, 14945618, 516.2456717
                1099, 230, 18488231, 491.1467339
                1108, 803, 10233925, 518.4355252
                  1109, 175, 6360, 574.7375700
                1135, 352, 13974904, 514.4139422
Warning,  computation interrupted
> g;
                              1143
> for g from 1143 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1153, 786, 14157019, 523.0775017
               1154, 119, 108393065, 502.8290870
               1154, 1035, 54196532, 505.6657483
                1184, 965, 18409238, 522.6929761
                  1186, 815, 889, 452.0273380
                1214, 195, 43120767, 532.2204842
               1214, 1019, 21560383, 522.9005011
                 1229, 1219, 7750, 570.8339409
Warning,  computation interrupted
> g;
                              1252
> for g from 1252 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                  1257, 776, 462, 462.0768193
                1259, 315, 21269244, 508.7887438
                1259, 944, 10634621, 519.9470085
                1262, 127, 43643984, 520.4147884
               1262, 1135, 87287969, 513.6562182
                 1265, 696, 16141, 571.0616420
Warning,  computation interrupted
> g;
                              1280
> for g from 1280 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1282, 613, 20708451, 511.5312822
                1282, 669, 10354225, 519.3672080
                1289, 191, 10567610, 534.1366935
                1290, 329, 10266287, 518.6864184
                1311, 151, 11442740, 525.5356545
                1313, 766, 10844640, 530.9019392
                1319, 537, 17429270, 509.4353345
                1319, 782, 34858540, 515.9387315
                  1325, 632, 191, 462.8105520
                  1327, 898, 3693, 570.2622500
               1333, 1028, 18163167, 519.6304161
                1347, 215, 13234822, 512.8737125
Warning,  computation interrupted
> g;
                              1352
> for g from 1352 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                  1357, 972, 7837, 570.5700480
                1369, 430, 10084177, 523.3670233
                1373, 71, 11039926, 515.5052365
                1413, 800, 15997258, 506.5514780
                1417, 34, 132436187, 522.2517025
               1417, 1383, 66218093, 523.2915442
                 1420, 179, 10864, 571.2051889
                 1420, 541, 10488, 572.1974380
                1423, 521, 74261128, 521.4453519
               1423, 902, 148522257, 514.8929213
                1424, 635, 13895242, 503.9737079
                1424, 789, 27790484, 535.4640029
                1425, 407, 88159046, 515.1716432
               1425, 1018, 44079523, 506.7079139
                 1427, 870, 74818, 579.7441750
               1429, 1109, 13493088, 532.4680511
                1432, 663, 36822681, 526.3901020
                1432, 769, 18411340, 543.8196616
               1432, 1409, 18249099, 527.2200023
                1433, 352, 28079914, 506.0815157
               1433, 1081, 14039957, 516.7040986
                1435, 662, 73235551, 507.0612593
               1435, 773, 146471103, 539.3709543
Warning,  computation interrupted
> for g from 1435 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1435, 662, 73235551, 507.0612593
               1435, 773, 146471103, 539.3709543
Warning,  computation interrupted
> g;
                              1458
> for g from 1458 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1465, 49, 45278429, 539.5211399
               1465, 1416, 90556859, 518.7375127
                  1466, 289, 368, 462.8809950
                 1471, 1148, 38173, 570.0043833
Warning,  computation interrupted
> g;
                              1474
> for g from 1474 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1487, 441, 10881239, 508.7240218
                1487, 676, 11652349, 513.1931422
               1487, 1046, 21762478, 512.1594097
                  1503, 1310, 255, 464.4177274
Warning,  computation interrupted
> g;
                              1520
> for g from 1520 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1525, 829, 11592963, 500.3021241
                  1533, 61, 12208, 574.9691909
                1533, 79, 21377130, 513.4280256
               1533, 1454, 42754262, 523.3113463
                  1534, 993, 1766, 573.2571174
                1535, 384, 81045534, 514.3551453
               1535, 1151, 40522766, 513.9517261
                 1538, 751, 17871, 576.1738422
Warning,  computation interrupted
> g;
                              1541
> for g from 1541 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1543, 363, 33376146, 513.4541675
               1543, 1180, 16688072, 517.3704380
                1544, 107, 24745061, 510.5792596
               1544, 1437, 12372530, 521.7098871
Warning,  computation interrupted
> g;
                              1560
> for g from 1560 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1561, 529, 57845988, 517.0861201
               1561, 1032, 28922994, 495.3919551
               1565, 176, 123900774, 516.6400037
                1565, 322, 34875718, 528.7418483
               1565, 1243, 17437859, 523.4985572
               1565, 1389, 61950386, 510.5521536
                1570, 59, 11943753, 515.7918405
Warning,  computation interrupted
> g;
                              1583
> for g from 1583 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                  1587, 857, 5348, 571.0094411
Warning,  computation interrupted
> g;
                              1599
> for g from 1599 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1618, 345, 15537609, 539.7860126
                1625, 123, 11564215, 498.8769664
               1625, 1502, 23128430, 499.0663140
                  1635, 49, 14617, 571.0310807
                 1635, 1327, 19296, 574.0549086
                1637, 302, 20822598, 514.4795159
               1637, 1335, 10411299, 517.0816790
                1639, 703, 50022187, 522.2911317
                1639, 936, 25011093, 523.8163426
                1645, 43, 113164748, 540.0975633
               1645, 1602, 56582374, 549.0312006
Warning,  computation interrupted
> g;
                              1650
> for g from 1650 to 1670 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
> g;
                              1671
> for g from 1671 to 1860 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1685, 137, 15360161, 495.3928836
               1685, 1333, 11617844, 512.4307903
               1685, 1548, 30720324, 510.1710736
                1687, 760, 14841367, 523.5416466
                1687, 927, 29682735, 516.1907530
                1694, 201, 10135176, 503.5610673
               1698, 271, 280152992, 520.1298821
               1698, 1427, 560305985, 502.5773677
                  1706, 901, 5972, 575.0516400
                1707, 73, 12805110, 518.1281446
               1709, 1031, 14276229, 503.7982924
Warning,  computation interrupted
> g;
                              1709
> for g from 1709 to 1860 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
               1709, 1031, 14276229, 503.7982924
                1731, 680, 22736473, 507.4046786
               1731, 1051, 45472946, 511.1347805
                1739, 315, 19020802, 519.9345373
               1739, 1424, 38041604, 527.3833513
               1753, 1371, 11552788, 541.7682468
                1765, 722, 30350948, 543.0578356
               1765, 1043, 15175473, 523.0145238
Warning,  computation interrupted
> g;
                              1767
> for g from 1767 to 1860 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1770, 797, 16860582, 527.6838153
                1770, 973, 33721165, 508.1269246
                1774, 279, 14776279, 525.2120144
                1778, 571, 39359583, 533.6754328
               1778, 1207, 78719167, 536.8675016
               1781, 1246, 11666385, 516.1392266
                  1783, 198, 1275, 575.1517966
               1783, 735, 176315433, 526.7980357
               1783, 1048, 88157716, 532.1734197
                 1801, 126, 118348, 571.3760816
                  1803, 929, 6284, 571.3577700
               1804, 1237, 11729848, 483.2546977
Warning,  computation interrupted
> g;
                              1823
> for g from 1823 to 1870 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1829, 78, 30727058, 510.6711042
                1829, 255, 53835193, 519.4337246
               1829, 1574, 26917596, 530.7376530
               1829, 1751, 61454117, 532.9602514
                  1835, 1007, 858, 464.9009247
                1841, 205, 15173850, 498.9683828
               1852, 1097, 10604262, 508.4102701
Warning,  computation interrupted
> g;
                              1854
> for g from 1854 to 1870 do
> for r from 1 to g-1 do
> if gcd(r,g)=1 then
> n2pB := evalf(2^(r/g)):
> ncf2B := cfrac( n2pB, 1000, 'quotients');
> ncf2C := subsop(nops(ncf2B) = NULL, ncf2B);
> ncf2Max := max(op(ncf2C));
> ncf2Size := evalf[10](log10(nthdenom(ncf2B,1000)));
> if ncf2Max > 10^7 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size > 570 then 
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> if ncf2Size < 465 then
> print(g, r, max(op(ncf2C)), ncf2Size);
> end if;
> end if;
> end do:
> end do:
                1861, 905, 26575669, 537.5257548
                1861, 956, 13287834, 523.8284360
> g;
                              1871
> 
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