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A283773 Numbers k such that U(k) = 1 mod 3, where U = A001950 = upper Wythoff sequence.

%I A283773 #12 Dec 06 2019 16:24:22
%S A283773 3,4,5,11,12,13,19,20,27,28,35,36,42,43,44,50,51,52,58,59,60,66,67,68,
%T A283773 74,75,82,83,90,91,97,98,99,105,106,107,113,114,115,121,122,123,129,
%U A283773 130,137,138,144,145,146,152,153,154,160,161,162,168,169,170,176
%N A283773 Numbers k such that U(k) = 1 mod 3, where U = A001950 = upper Wythoff sequence.
%C A283773 The sequences A283772, A283773, A283774 partition the positive integers.
%H A283773 Clark Kimberling, <a href="/A283773/b283773.txt">Table of n, a(n) for n = 1..10000</a>
%F A283773 a(n+1) - a(n) is in {1,6,7} for every n.
%t A283773 r = GoldenRatio^2; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];
%t A283773 Flatten[Position[u, 0]]  (* A283772 *)
%t A283773 Flatten[Position[u, 1]]  (* A283773 *)
%t A283773 Flatten[Position[u, 2]]  (* A283774 *)
%o A283773 (PARI) r = (3 + sqrt(5))/2;
%o A283773 for(n=1, 351, if(floor(n*r)%3==1, print1(n,", "))) \\ _Indranil Ghosh_, Mar 19 2017
%o A283773 (Python)
%o A283773 import math
%o A283773 from sympy import sqrt
%o A283773 r = (3 + sqrt(5))/2
%o A283773 [n for n in range(1, 351) if int(math.floor(n*r))%3==1] # _Indranil Ghosh_, Mar 19 2017
%Y A283773 Cf. A000201, A001622, A283772, A283774.
%K A283773 nonn,easy
%O A283773 1,1
%A A283773 _Clark Kimberling_, Mar 18 2017