A283772 - OEIS

%I #11 Dec 06 2019 16:24:15

%S 6,7,14,15,21,22,23,29,30,31,37,38,39,45,46,47,53,54,61,62,69,70,76,

%T 77,78,84,85,86,92,93,94,100,101,102,108,109,116,117,124,125,131,132,

%U 133,139,140,141,147,148,149,155,156,157,163,164,171,172,179,180

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

%C The sequences A283772, A283773, A283774 partition the positive integers.

%H Clark Kimberling, <a href="/A283772/b283772.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n+1) - a(n) is in {1,6,7} for every n.

%t r = GoldenRatio^2; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];

%t Flatten[Position[u, 0]]  (* A283772 *)

%t Flatten[Position[u, 1]]  (* A283773 *)

%t Flatten[Position[u, 2]]  (* A283774 *)

%o (PARI) r = (3 + sqrt(5))/2;

%o for(n=1, 351, if(floor(n*r)%3==0, print1(n,", "))) \\ _Indranil Ghosh_, Mar 19 2017

%o (Python)

%o import math

%o from sympy import sqrt

%o r = (3 + sqrt(5))/2

%o [n for n in range(1, 351) if int(math.floor(n*r))%3==0] # _Indranil Ghosh_, Mar 19 2017

%Y Cf. A000201, A001622, A283773, A283774.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Mar 18 2017