A161872 Smallest unhappy number in base n (or 0 if no unhappy numbers in the base).

0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 7, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

2,2

Comments

All positive integers are happy numbers in base 2 and base 4; they are called "happy bases". There are no other happy bases < 500,000,000.

Links

Antti Karttunen, Table of n, a(n) for n = 2..10082

Antti Karttunen, Data supplement: n, a(n) computed for n = 2..100000

Dino Lorenzini, Mentzelos Melistas, Arvind Suresh, Makoto Suwama, and Haiyang Wang, Integer Dynamics, arXiv:2105.14361 [math.NT], 2021.

Mathematica

Table[If[MemberQ[{2, 4}, n], 0, Block[{k = 2}, While[NestWhile[Total[IntegerDigits[#, n]^2] &, k, UnsameQ, All] == 1, k++]; k]], {n, 2, 105}] (* Michael De Vlieger, Nov 06 2018 *)

Prog

(PARI) A161872(n) = if((2==n)||(4==n), 0, for(k=2, oo, my(visited = Map(), t = k); while(t!=1, if(mapisdefined(visited, t), return(k), mapput(visited, t, t)); t = vecsum(apply(d -> (d*d), digits(t, n)))))); \\ Antti Karttunen, Nov 06 2018

Crossrefs

Cf. A031177 (Unhappy numbers in base 10).

Sequence in context: A044948 A044949 A044950 * A278248 A036461 A244478

Adjacent sequences: A161869 A161870 A161871 * A161873 A161874 A161875

Keyword

nonn

Author

Jud McCranie, Jun 20 2009

Status

approved