LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Strings of Consecutive Happy Numbers 1 March 200815 Aug 200824 Sept 200825 Mar 200911 July 2009We need a procedure, given n, to find the minimal N such that S(N) = n. In our text explanations, we will denote this minimal N by L(n). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic=QyQ+SSJmRzYiZio2I0kibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQ5JCIiI0YlRiVGJSIiIg==QyQ+SSNic0c2IiIjNSIiIg==QyQ+SShvbmVzdGVwRzYiZio2I0kjbjFHRiU2JUkkYW5zR0YlSSJuR0YlSSJkR0YlRiVGJUMmPjglOSQ+OCQiIiE/KEYlIiIiRjVGJTJGM0YvQyU+OCYtSSRtb2RHRiU2JEYvSSNic0dGJT5GMiwmRjJGNS1JImZHRiU2I0Y5RjU+Ri8qJiwmRi9GNUY5ISIiRjVGPUZGRjJGJUYlRiVGNQ==QyQ+SSZoYXBweUc2ImYqNiNJIm5HRiU2JUkibUdGJUkiakdGJUknaGVpZ2h0R0YlRiVGJUMnPjgkOSQ+OCYhIiI/KDglIiIiRjYiJCsiMzJGNkYvMEYvIiIlPkYvLUkob25lc3RlcEdGJTYjRi9AJC9GL0Y2PkYyRjVGMkYlRiVGJUY2Given the values for L(k) for all k<n, we will bootstrap ourselves to find the next value of L(n). To do this, we try all possible final digits of L(n), and take the best candidate. First, we need a procedure that will add the trial digit to the number and sort the digits. QyQ+SS5BZGRTb3J0RGlnaXRzRzYiZio2JEkiYUdGJUkiZEdGJTYlSSJiR0YlSSJlR0YlSSJpR0YlRiVGJUMqPjgkOSQ+OCU3Ij8oRiUiIiJGNkYlMiIiIUYwQyQ+RjM3JC1JJG1vZEdGJTYkRjBJI2JzR0YlLUkjb3BHJSpwcm90ZWN0ZWRHNiNGMz5GMC1JJWlxdW9HRkI2JCwmRjBGNkY8ISIiRj8+RjM3JEZAOSU+RjMtSSVzb3J0R0ZCRkM+RjBGOD8oOCZGNkY2LUklbm9wc0dGQkZDSSV0cnVlR0ZCPkYwLCYqJkYwRjZGP0Y2RjYmRjM2I0ZSRjZGMEYlRiVGJUY2LUkuQWRkU29ydERpZ2l0c0c2IjYkIiZPayQiIiU=Now we initialize our list of least values.QyQ+SSJBRzYiNysiIiIiIzYiJDYiIiIjIiM3IiQ3IiIlNzYiI0EiIiRGJw==QyY/KEkibkc2IiIjNSIiIiIjOkkldHJ1ZUclKnByb3RlY3RlZEdDJT5JIkxHRiUtSS5BZGRTb3J0RGlnaXRzR0YlNiQmSSJBR0YlNiMsJkYkRichIiJGJ0YnPyhJImRHRiUiIiNGJyIiJEYpQyQ+SSJNR0YlLUYvNiQmRjI2IywmRiRGJy1JKG9uZXN0ZXBHRiU2I0Y3RjVGN0AkMkY8Ri0+Ri1GPD5GMjckLUkjb3BHRio2I0YyRi1GNUYyRic=QyQ+SSJBRzYiNyQtSSNvcEclKnByb3RlY3RlZEc2I0YkIiIlIiIiQyY/KEkibkc2IiIjPCIiIiIjQ0kldHJ1ZUclKnByb3RlY3RlZEdDJT5JIkxHRiUtSS5BZGRTb3J0RGlnaXRzR0YlNiQmSSJBR0YlNiMsJkYkRichIiJGJ0YnPyhJImRHRiUiIiNGJyIiJUYpQyQ+SSJNR0YlLUYvNiQmRjI2IywmRiRGJy1JKG9uZXN0ZXBHRiU2I0Y3RjVGN0AkMkY8Ri0+Ri1GPD5GMjckLUkjb3BHRio2I0YyRi1GNUYyRic=QyQ+SSJBRzYiNyQtSSNvcEclKnByb3RlY3RlZEc2I0YkIiImIiIiQyY/KEkibkc2IiIjRSIiIiIjTkkldHJ1ZUclKnByb3RlY3RlZEdDJT5JIkxHRiUtSS5BZGRTb3J0RGlnaXRzR0YlNiQmSSJBR0YlNiMsJkYkRichIiJGJ0YnPyhJImRHRiUiIiNGJyIiJkYpQyQ+SSJNR0YlLUYvNiQmRjI2IywmRiRGJy1JKG9uZXN0ZXBHRiU2I0Y3RjVGN0AkMkY8Ri0+Ri1GPD5GMjckLUkjb3BHRio2I0YyRi1GNUYyRic=QyQ+SSJBRzYiNyQtSSNvcEclKnByb3RlY3RlZEc2I0YkIiInIiIiQyQ/KEkibkc2IiIjUCIiIiIjW0kldHJ1ZUclKnByb3RlY3RlZEdDJT5JIkxHRiUtSS5BZGRTb3J0RGlnaXRzR0YlNiQmSSJBR0YlNiMsJkYkRichIiJGJ0YnPyhJImRHRiUiIiNGJyIiJ0YpQyQ+SSJNR0YlLUYvNiQmRjI2IywmRiRGJy1JKG9uZXN0ZXBHRiU2I0Y3RjVGN0AkMkY8Ri0+Ri1GPD5GMjckLUkjb3BHRio2I0YyRi1GNQ==QyQ+SSJBRzYiNyQtSSNvcEclKnByb3RlY3RlZEc2I0YkIiIoIiIiQyQ/KEkibkc2IiIjXSIiIiIjakkldHJ1ZUclKnByb3RlY3RlZEdDJT5JIkxHRiUtSS5BZGRTb3J0RGlnaXRzR0YlNiQmSSJBR0YlNiMsJkYkRichIiJGJ0YnPyhJImRHRiUiIiNGJyIiKEYpQyQ+SSJNR0YlLUYvNiQmRjI2IywmRiRGJy1JKG9uZXN0ZXBHRiU2I0Y3RjVGN0AkMkY8Ri0+Ri1GPD5GMjckLUkjb3BHRio2I0YyRi1GNQ==QyQ+SSJBRzYiNyQtSSNvcEclKnByb3RlY3RlZEc2I0YkIiIpIiIiQyQ/KEkibkc2IiIjbCIiIiIjISlJJXRydWVHJSpwcm90ZWN0ZWRHQyU+SSJMR0YlLUkuQWRkU29ydERpZ2l0c0dGJTYkJkkiQUdGJTYjLCZGJEYnISIiRidGJz8oSSJkR0YlIiIjRiciIilGKUMkPkkiTUdGJS1GLzYkJkYyNiMsJkYkRictSShvbmVzdGVwR0YlNiNGN0Y1RjdAJDJGPEYtPkYtRjw+RjI3JC1JI29wR0YqNiNGMkYtRjU=QyQ+SSJBRzYiNyQtSSNvcEclKnByb3RlY3RlZEc2I0YkIiIqIiIiTo find how far we need to go we use our maximal length single-digit numbers 1112223344456667778888888LUkob25lc3RlcEc2IjYjIjopKSkpKSl5eG1jV01CQTYiQyQ/KEkibkc2IiIjIykiIiIiJCsqSSV0cnVlRyUqcHJvdGVjdGVkR0MlPkkiTEdGJS1JLkFkZFNvcnREaWdpdHNHRiU2JCZJIkFHRiU2IywmRiRGJyEiIkYnRic/KEkiZEdGJSIiI0YnIiIqRilDJD5JIk1HRiUtRi82JCZGMjYjLCZGJEYnLUkob25lc3RlcEdGJTYjRjdGNUY3QCQyRjxGLT5GLUY8PkYyNyQtSSNvcEdGKjYjRjJGLUY1QyRJIkFHNiIiIiI=We now find the biggest number with a given digit. 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYjLUkjbW5HRiQ2JFEkNDQ5RicvRjNRJ25vcm1hbEYnRj4vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=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In particular, if n>448, then L(n) must have the digit 9 in it. 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QyQ+SSVsb3dTRzYiSSJBR0YlIiIiWe now verify a result we need for analyzing large values, namely, that for n1>367 and n2>n1+108, then L(n2) >= L(n1) + 431000. 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We next analyze another result we need for large values, namely, that for n1 > 20, if L(n1) > L(n2) then L(L(n1)) > L(L(n2))+10^6. we already know that if the values are over 378 and the difference over 108, then we are OK. 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, the minimalbigN module was badly defined with an inconsistent datatype. So we redefine it here for the next calculation. 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEvTkVXbWluaW1hbGJpZ05GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRJDI2NUYnL0YzUSdub3JtYWxGJ0Y+LUkjbW9HRiQ2LVEiO0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRi8lKnN5bW1ldHJpY0dGRi8lKGxhcmdlb3BHRkYvJS5tb3ZhYmxlbGltaXRzR0ZGLyUnYWNjZW50R0ZGLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGKy1GNjYkLUYjNiMtRjs2JFEkNjc4RidGPkY+RkA=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEvTkVXbWluaW1hbGJpZ05GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRIzY4RicvRjNRJ25vcm1hbEYnRj4tSSNtb0dGJDYtUSI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEob25lc3RlcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUkjbW5HRiQ2JFEjMjhGJy9GM1Enbm9ybWFsRidGPg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH