A001273 - OEIS

%I #39 Jan 05 2025 19:51:31

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

%N Smallest number that takes n steps to reach 1 under iteration of sum-of-squares-of-digits map (= smallest "happy number" of height n).

%C Subsequent terms are too large to display in full.

%C a(8) = 3789 * 10^973 - 1 (3788 followed by 973 9's).

%C 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).

%C a(10) = 259 * 10^((a(9) - 93)/81) - 1.

%C a(11) = 179 * 10^((a(10) - 114)/81) - 1.

%C a(12) = 47 * 10^((a(11) - 52)/81) - 1.

%D Richard K. Guy, Unsolved Problems in Number Theory, Sect. E34. (2nd ed. UPINT2 = 1994, 3rd ed. UPINT3 = 2004)

%H Tianxin Cai and Xia Zhou, <a href="http://projecteuclid.org/euclid.rmjm/1225114174">On The Heights of Happy Numbers</a>, Rocky Mountain J. Math., Vol. 38, No. 6 (2008), 1921-1926.

%H H. G. Grundman and E. A. Teeple, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/41-4.html">Heights of happy numbers and cubic happy numbers</a>, Fib Quart. 41 (4) (2003) 301

%H Hans Havermann, <a href="http://chesswanks.com/blahg/odo/Blog/Entries/2010/5/2_Big_and_happy.html">Big and Happy</a>

%H Gabriel Lapointe, <a href="https://arxiv.org/abs/1904.12032">On finding the smallest happy numbers of any heights</a>, arXiv:1904.12032 [math.NT], 2019.

%H May Mei and Andrew Read-McFarland, <a href="http://arxiv.org/abs/1511.01441">Numbers and the Heights of their Happiness</a>, arXiv:1511.01441 [math.NT], 2015.

%Y Cf. A007770, A018785, A176762.

%K nonn,base

%O 0,2

%A _N. J. A. Sloane_

%E a(7), a(8) from _Jud McCranie_, Sep 15 1994

%E a(9)-a(12) from _Hans Havermann_, May 02 2010

%E Edited by _Hans Havermann_, May 03 2010, May 04 2010