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A300081 a(n) is the number of steps needed to reach 1 or 89 under iteration of sum-of-squares-of-digits map.

%I A300081 #25 Feb 16 2025 08:33:53
%S A300081 0,5,7,4,4,9,5,5,6,1,6,5,2,6,6,3,5,5,4,5,5,6,3,6,3,5,6,3,2,7,2,3,6,4,
%T A300081 5,8,2,3,7,4,6,6,4,4,7,4,5,6,4,4,6,3,5,7,5,4,6,1,4,9,3,5,8,4,4,7,2,2,
%U A300081 8,5,5,6,2,5,6,2,9,8,3,5,5,3,3,6,1,2,8,10,0
%N A300081 a(n) is the number of steps needed to reach 1 or 89 under iteration of sum-of-squares-of-digits map.
%C A300081 By the definition, a(1) = a(89) = 0.
%H A300081 Seiichi Manyama, <a href="/A300081/b300081.txt">Table of n, a(n) for n = 1..10000</a>
%H A300081 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HappyNumber.html">Happy Number</a>
%H A300081 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnhappyNumber.html">Unhappy Number</a>
%H A300081 Wikipedia, <a href="http://en.wikipedia.org/wiki/Happy_number">Happy number</a>
%e A300081 n|  0     1     2     3     4     5     6     7     8     9
%e A300081 -----------------------------------------------------------
%e A300081 2|  2 ->  4 -> 16 -> 37 -> 58 -> 89.
%e A300081 3|  3 ->  9 -> 81 -> 65 -> 61 -> 37 -> 58 -> 89.
%e A300081 4|  4 -> 16 -> 37 -> 58 -> 89.
%e A300081 5|  5 -> 25 -> 29 -> 85 -> 89.
%e A300081 6|  6 -> 36 -> 45 -> 41 -> 17 -> 50 -> 25 -> 29 -> 85 -> 89.
%o A300081 (PARI) f(n) = {my(d = digits(n)); sum(k=1, #d, d[k]^2);}
%o A300081 a(n) = {my(nb = 0, fn = n); while (! ((n == 1) || (n == 89)), n = f(n); nb++); nb;} \\ _Michel Marcus_, Feb 25 2018
%Y A300081 Cf. A003621, A007770.
%K A300081 nonn,base
%O A300081 1,2
%A A300081 _Seiichi Manyama_, Feb 24 2018