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A054966 Numbers that are congruent to {0, 1, 8} mod 9.

%I A054966 #25 Jul 19 2024 09:39:50
%S A054966 0,1,8,9,10,17,18,19,26,27,28,35,36,37,44,45,46,53,54,55,62,63,64,71,
%T A054966 72,73,80,81,82,89,90,91,98,99,100,107,108,109,116,117,118,125,126,
%U A054966 127,134,135,136,143,144,145,152,153,154,161,162,163,170,171,172,179,180
%N A054966 Numbers that are congruent to {0, 1, 8} mod 9.
%C A054966 n == n^3 mod 9, so the iterated sum of the decimal digits of n and n^3 are equal.
%D A054966 H. I. Okagbue, M.O.Adamu, S.A. Bishop and A.A. Opanuga, Properties of Sequences Generated by Summing the Digits of Cubed Positive Integers, Indian Journal Of Natural Sciences, Vol. 6 / Issue 32 / October 2015
%H A054966 Vincenzo Librandi, <a href="/A054966/b054966.txt">Table of n, a(n) for n = 1..1000</a>
%H A054966 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A054966 G.f.: x^2*(1+7*x+x^2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011
%F A054966 From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F A054966 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A054966 a(n) = 3*n-3+2*cos(2*n*Pi/3)+2*sin(2*n*Pi/3)/sqrt(3).
%F A054966 a(3k) = 9k-1, a(3k-1) = 9k-8, a(3k-2) = 9k-9. (End)
%F A054966 A008591 UNION A056020. - _R. J. Mathar_, Jul 19 2024
%F A054966 a(n) -a(n-1) = A105395(n+1), n>1. - _R. J. Mathar_, Jul 19 2024
%p A054966 A054966:=n->3*n-3+2*cos(2*n*Pi/3)+2*sin(2*n*Pi/3)/sqrt(3): seq(A054966(n), n=1..100); # _Wesley Ivan Hurt_, Jun 14 2016
%t A054966 Select[Range[0, 200], MemberQ[{0, 1, 8}, Mod[#, 9]] &] (* _Wesley Ivan Hurt_, Jun 14 2016 *)
%t A054966 LinearRecurrence[{1, 0, 1, -1}, {0, 1, 8, 9}, 100] (* _Vincenzo Librandi_, Jun 15 2016 *)
%o A054966 (Magma) [n : n in [0..200] | n mod 9 in [0, 1, 8]]; // _Wesley Ivan Hurt_, Jun 14 2016
%Y A054966 Cf. A047523. Complement of A275910.
%K A054966 nonn,easy
%O A054966 1,3
%A A054966 _Henry Bottomley_, May 24 2000