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

6, 7, 14, 15, 21, 22, 23, 29, 30, 31, 37, 38, 39, 45, 46, 47, 53, 54, 61, 62, 69, 70, 76, 77, 78, 84, 85, 86, 92, 93, 94, 100, 101, 102, 108, 109, 116, 117, 124, 125, 131, 132, 133, 139, 140, 141, 147, 148, 149, 155, 156, 157, 163, 164, 171, 172, 179, 180

Offset: 1

Author

Clark Kimberling, Mar 18 2017

Keywords

• nonn
• easy

Comments

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

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000201, A001622, A283773, A283774.

Programs

Mathematica

r = GoldenRatio^2; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];
Flatten[Position[u, 0]]  (* A283772 *)
Flatten[Position[u, 1]]  (* A283773 *)
Flatten[Position[u, 2]]  (* A283774 *)

PARI

r = (3 + sqrt(5))/2;
for(n=1, 351, if(floor(n*r)%3==0, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

Python

import math
from sympy import sqrt
r = (3 + sqrt(5))/2
[n for n in range(1, 351) if int(math.floor(n*r))%3==0] # Indranil Ghosh, Mar 19 2017

Formula

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