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A001273 Smallest number that takes n steps to reach 1 under iteration of sum-of-squares-of-digits map (= smallest "happy number" of height n). 6
1, 10, 13, 23, 19, 7, 356, 78999 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Subsequent terms are too large to display in full.
a(8) = 3789 * 10^973 - 1 (3788 followed by 973 9's).
a(9) = 78889 * 10^((a(8) - 305)/81) - 1 (78888 followed by (421 * 10^973 - 34)/9 9's, specified by Warut Roonguthai for UPINT3).
a(10) = 259 * 10^((a(9) - 93)/81) - 1.
a(11) = 179 * 10^((a(10) - 114)/81) - 1.
a(12) = 47 * 10^((a(11) - 52)/81) - 1.
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, Sect. E34. (2nd ed. UPINT2 = 1994, 3rd ed. UPINT3 = 2004)
LINKS
Tianxin Cai and Xia Zhou, On The Heights of Happy Numbers, Rocky Mountain J. Math., Vol. 38, No. 6 (2008), 1921-1926.
H. G. Grundman and E. A. Teeple, Heights of happy numbers and cubic happy numbers, Fib Quart. 41 (4) (2003) 301
Hans Havermann, Big and Happy
Gabriel Lapointe, On finding the smallest happy numbers of any heights, arXiv:1904.12032 [math.NT], 2019.
May Mei and Andrew Read-McFarland, Numbers and the Heights of their Happiness, arXiv:1511.01441 [math.NT], 2015.
CROSSREFS
Sequence in context: A191969 A018785 A176762 * A111524 A074346 A126973
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
a(7), a(8) from Jud McCranie, Sep 15 1994
a(9)-a(12) from Hans Havermann, May 02 2010
Edited by Hans Havermann, May 03 2010, May 04 2010
STATUS
approved

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Last modified July 17 09:24 EDT 2024. Contains 374363 sequences. (Running on oeis4.)