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A283774 Numbers k such that U(k) == 2 mod 3, where U = A001950 = upper Wythoff sequence.

%I A283774 #13 Dec 06 2019 16:24:28
%S A283774 1,2,8,9,10,16,17,18,24,25,26,32,33,34,40,41,48,49,55,56,57,63,64,65,
%T A283774 71,72,73,79,80,81,87,88,89,95,96,103,104,110,111,112,118,119,120,126,
%U A283774 127,128,134,135,136,142,143,150,151,158,159,165,166,167,173
%N A283774 Numbers k such that U(k) == 2 mod 3, where U = A001950 = upper Wythoff sequence.
%C A283774 The sequences A283772, A283773, A283774 partition the positive integers.
%H A283774 Clark Kimberling, <a href="/A283774/b283774.txt">Table of n, a(n) for n = 1..10000</a>
%F A283774 a(n+1) - a(n) is in {1,6,7} for every n.
%t A283774 r = GoldenRatio^2; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];
%t A283774 Flatten[Position[u, 0]]  (* A283772 *)
%t A283774 Flatten[Position[u, 1]]  (* A283773 *)
%t A283774 Flatten[Position[u, 2]]  (* A283774 *)
%o A283774 (PARI) r = (3 + sqrt(5))/2;
%o A283774 for(n=1, 351, if(floor(n*r)%3==2, print1(n, ", "))) \\ _Indranil Ghosh_, Mar 21 2017
%o A283774 (Python)
%o A283774 import math
%o A283774 from sympy import sqrt
%o A283774 r = (3 + sqrt(5))/2
%o A283774 [n for n in range(1, 351) if int(math.floor(n*r))%3==2] # _Indranil Ghosh_, Mar 21 2017
%Y A283774 Cf. A000201, A001622, A283772, A283774.
%K A283774 nonn,easy
%O A283774 1,2
%A A283774 _Clark Kimberling_, Mar 19 2017