A283774 - OEIS

%I #13 Dec 06 2019 16:24:28

%S 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 71,72,73,79,80,81,87,88,89,95,96,103,104,110,111,112,118,119,120,126,

%U 127,128,134,135,136,142,143,150,151,158,159,165,166,167,173

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

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

%H Clark Kimberling, <a href="/A283774/b283774.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==2, print1(n, ", "))) \\ _Indranil Ghosh_, Mar 21 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==2] # _Indranil Ghosh_, Mar 21 2017

%Y Cf. A000201, A001622, A283772, A283774.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Mar 19 2017