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%I #14 Sep 10 2021 18:29:26
%S 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,
%T 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,
%U 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
%N Smallest unhappy number in base n (or 0 if no unhappy numbers in the base).
%C 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.
%H Antti Karttunen, <a href="/A161872/b161872.txt">Table of n, a(n) for n = 2..10082</a>
%H Antti Karttunen, <a href="/A161872/a161872.txt">Data supplement: n, a(n) computed for n = 2..100000</a>
%H Dino Lorenzini, Mentzelos Melistas, Arvind Suresh, Makoto Suwama, and Haiyang Wang, <a href="https://arxiv.org/abs/2105.14361">Integer Dynamics</a>, arXiv:2105.14361 [math.NT], 2021.
%t 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 *)
%o (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
%Y Cf. A031177 (Unhappy numbers in base 10).
%K nonn
%O 2,2
%A _Jud McCranie_, Jun 20 2009
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