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%I #12 Dec 19 2017 18:37:25
%S 2,4,5,7,11,13,14,16,20,22,23,25,29,31,32,34,38,40,41,43,47,49,50,52,
%T 56,58,59,61,65,67,68,70,74,76,77,79,83,85,86,88,92,94,95,97,101,103,
%U 104,106,110,112,113,115,119,121,122,124,128,130,131,133,137,139,140
%N Numbers where iterated sum of digits of square settles down to a cyclic pattern (in fact 13, 16, 13, 16, ...).
%C Numbers == 2, 4, 5 or 7 mod 9, i.e. such that n^4 is not congruent to n^2 mod 9.
%C Numbers congruent to {2, 4, 5, 7} mod 9.
%H Colin Barker, <a href="/A056527/b056527.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1).
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - _Harvey P. Dale_, Apr 05 2015
%F From _Colin Barker_, Dec 19 2017: (Start)
%F G.f.: x*(2 + 2*x + x^2 + 2*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
%F a(n) = (-9 + (-1)^(1+n) - (3-3*i)*(-i)^n - (3+3*i)*i^n + 18*n) / 8 where i=sqrt(-1).
%F (End)
%e a(1)=2 because iteration starts 2, 4, 7, 13, 16, 13, 16, ....
%t Flatten[Table[9n+{2,4,5,7},{n,0,20}]] (* or *) LinearRecurrence[{1,0,0,1,-1},{2,4,5,7,11},100] (* _Harvey P. Dale_, Apr 05 2015 *)
%o (PARI) Vec(x*(2 + 2*x + x^2 + 2*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^80)) \\ _Colin Barker_, Dec 19 2017
%Y Cf. A004159 for sum of digits of square, A056020 where iteration settles to 1, A056020 where iteration settles to 9, also A056528, A056529. Unhappy numbers A031177 deal with iteration of square of sum of digits not settling to a single result.
%K base,easy,nonn
%O 1,1
%A _Henry Bottomley_, Jun 19 2000
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