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 A056527 Numbers where iterated sum of digits of square settles down to a cyclic pattern (in fact 13, 16, 13, 16, ...). 4
 2, 4, 5, 7, 11, 13, 14, 16, 20, 22, 23, 25, 29, 31, 32, 34, 38, 40, 41, 43, 47, 49, 50, 52, 56, 58, 59, 61, 65, 67, 68, 70, 74, 76, 77, 79, 83, 85, 86, 88, 92, 94, 95, 97, 101, 103, 104, 106, 110, 112, 113, 115, 119, 121, 122, 124, 128, 130, 131, 133, 137, 139, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers == 2, 4, 5 or 7 mod 9, i.e. such that n^4 is not congruent to n^2 mod 9. Numbers congruent to {2, 4, 5, 7} mod 9. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1, -1). FORMULA a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Harvey P. Dale, Apr 05 2015 From Colin Barker, Dec 19 2017: (Start) G.f.: x*(2 + 2*x + x^2 + 2*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)). a(n) = (-9 + (-1)^(1+n) - (3-3*i)*(-i)^n - (3+3*i)*i^n + 18*n) / 8 where i=sqrt(-1). (End) EXAMPLE a(1)=2 because iteration starts 2, 4, 7, 13, 16, 13, 16, .... MATHEMATICA 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 *) PROG (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 CROSSREFS 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. Sequence in context: A255850 A108464 A128815 * A147991 A033160 A110924 Adjacent sequences:  A056524 A056525 A056526 * A056528 A056529 A056530 KEYWORD base,easy,nonn AUTHOR Henry Bottomley, Jun 19 2000 STATUS approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)