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A283772 Numbers k such that U(k) = 0 mod 3, where U = A001950 = upper Wythoff sequence.

%I A283772 #11 Dec 06 2019 16:24:15
%S A283772 6,7,14,15,21,22,23,29,30,31,37,38,39,45,46,47,53,54,61,62,69,70,76,
%T A283772 77,78,84,85,86,92,93,94,100,101,102,108,109,116,117,124,125,131,132,
%U A283772 133,139,140,141,147,148,149,155,156,157,163,164,171,172,179,180
%N A283772 Numbers k such that U(k) = 0 mod 3, where U = A001950 = upper Wythoff sequence.
%C A283772 The sequences A283772, A283773, A283774 partition the positive integers.
%H A283772 Clark Kimberling, <a href="/A283772/b283772.txt">Table of n, a(n) for n = 1..10000</a>
%F A283772 a(n+1) - a(n) is in {1,6,7} for every n.
%t A283772 r = GoldenRatio^2; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];
%t A283772 Flatten[Position[u, 0]]  (* A283772 *)
%t A283772 Flatten[Position[u, 1]]  (* A283773 *)
%t A283772 Flatten[Position[u, 2]]  (* A283774 *)
%o A283772 (PARI) r = (3 + sqrt(5))/2;
%o A283772 for(n=1, 351, if(floor(n*r)%3==0, print1(n,", "))) \\ _Indranil Ghosh_, Mar 19 2017
%o A283772 (Python)
%o A283772 import math
%o A283772 from sympy import sqrt
%o A283772 r = (3 + sqrt(5))/2
%o A283772 [n for n in range(1, 351) if int(math.floor(n*r))%3==0] # _Indranil Ghosh_, Mar 19 2017
%Y A283772 Cf. A000201, A001622, A283773, A283774.
%K A283772 nonn,easy
%O A283772 1,1
%A A283772 _Clark Kimberling_, Mar 18 2017