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%I #8 Jul 11 2019 14:53:21
%S 4,2,11,113,78,58,29,16,4,2,9,3,36,6,29,16,4,2,9,3,36,6,29,16,4,2,9,3,
%T 36,6,29,16,4,2,9,3,36,6,29,16,4,2,9,3,36,6,29,16,4,2,9,3,36,6,29,16,
%U 4,2,9,3,36,6,29,16,4,2,9,3,36,6,29,16,4,2,9,3
%N Smallest unhappy number that takes n iterations of the sum of the squares of digits to reach 4, which is the smallest number of the unhappy numbers cycle.
%H Colin Barker, <a href="/A092952/b092952.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnhappyNumber.html">Unhappy Numbers</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).
%F From _Colin Barker_, Jul 11 2019: (Start)
%F G.f.: x*(4 + 2*x + 11*x^2 + 113*x^3 + 78*x^4 + 58*x^5 + 29*x^6 + 16*x^7 - 2*x^10 - 110*x^11 - 42*x^12 - 52*x^13) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).
%F a(n) = a(n-8) for n>8.
%F (End)
%e 113 is the fourth number of the sequence because it takes 4 iterations to reach 4: 113 / 1^2 + 1^2 + 3^2 = 11 / 1^2 + 1^2 = 2 / 2^2 = 4.
%o (PARI) Vec(x*(4 + 2*x + 11*x^2 + 113*x^3 + 78*x^4 + 58*x^5 + 29*x^6 + 16*x^7 - 2*x^10 - 110*x^11 - 42*x^12 - 52*x^13) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^80)) \\ _Colin Barker_, Jul 11 2019
%K nonn,base,easy
%O 1,1
%A _Sergio Pimentel_, Apr 23 2004
%E Edited by _Charles R Greathouse IV_, Aug 03 2010