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

1,1

Comments

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

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000201, A001622, A283773, A283774.

Sequence in context: A042315 A288667 A319487 * A080402 A146308 A047589

Adjacent sequences: A283769 A283770 A283771 * A283773 A283774 A283775

Keyword

nonn,easy

Author

Clark Kimberling, Mar 18 2017

Status

approved