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%I #22 Sep 08 2022 08:45:01
%S 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 72,73,80,81,82,89,90,91,98,99,100,107,108,109,116,117,118,125,126,
%U 127,134,135,136,143,144,145,152,153,154,161,162,163,170,171,172,179,180
%N Numbers that are congruent to {0, 1, 8} mod 9.
%C n == n^3 mod 9, so the iterated sum of the decimal digits of n and n^3 are equal.
%D 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 Vincenzo Librandi, <a href="/A054966/b054966.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F G.f.: x^2*(1+7*x+x^2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011
%F From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = 3*n-3+2*cos(2*n*Pi/3)+2*sin(2*n*Pi/3)/sqrt(3).
%F a(3k) = 9k-1, a(3k-1) = 9k-8, a(3k-2) = 9k-9. (End)
%p 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 Select[Range[0, 200], MemberQ[{0, 1, 8}, Mod[#, 9]] &] (* _Wesley Ivan Hurt_, Jun 14 2016 *)
%t LinearRecurrence[{1, 0, 1, -1}, {0, 1, 8, 9}, 100] (* _Vincenzo Librandi_, Jun 15 2016 *)
%o (Magma) [n : n in [0..200] | n mod 9 in [0, 1, 8]]; // _Wesley Ivan Hurt_, Jun 14 2016
%Y Cf. A047523. Complement of A275910.
%K nonn,easy
%O 1,3
%A _Henry Bottomley_, May 24 2000
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