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).

1, 10, 13, 23, 19, 7, 356, 78999

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

Table of n, a(n) for n=0..7.

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

Cf. A007770, A018785, A176762.

Sequence in context: A191969 A018785 A176762 * A111524 A074346 A126973

Adjacent sequences: A001270 A001271 A001272 * A001274 A001275 A001276

Keyword

nonn,base

Author

N. J. A. Sloane

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