Geodesic
Smallest examples of strings of consecutive happy numbers
Journal of integer sequences, Tome 13 (2010) no. 6.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A happy number $N$ is defined by the condition $S_{n}(N)= 1$ for some number $n$ of iterations of the function $S$, where $S(N)$ is the sum of the squares of the digits of $N$. Up to $10^{20}$, the longest known string of consecutive happy numbers was length five. We find the smallest string of consecutive happy numbers of length 6, 7, 8,$ \dots $, 13. For instance, the smallest string of six consecutive happy numbers begins with $N = 7899999999999959999999996$. We also find the smallest sequence of 3-consecutive cubic happy numbers of lengths 4, 5, 6, 7, 8, and 9.
Classification : 11A63
Keywords: happy number, cubic happy number 
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     author = {Styer, Robert},
     title = {Smallest examples of strings of consecutive happy numbers},
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     number = {6},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_6_a4/}
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Styer, Robert. Smallest examples of strings of consecutive happy numbers. Journal of integer sequences, Tome 13 (2010) no. 6. http://geodesic.mathdoc.fr/item/JIS_2010__13_6_a4/