A283769 Numbers k such that L(k) = 0 mod 3, where L = A000201 = lower Wythoff sequence.

2, 4, 6, 8, 13, 15, 17, 19, 21, 26, 28, 30, 32, 39, 41, 43, 45, 52, 54, 56, 58, 65, 67, 69, 71, 78, 80, 82, 84, 89, 91, 93, 95, 97, 102, 104, 106, 108, 110, 115, 117, 119, 121, 128, 130, 132, 134, 141, 143, 145, 147, 154, 156, 158, 160, 167, 169, 171, 173

Offset

1,1

Comments

The sequences A283769, A283770, A283771 partition the positive integers.

Links

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

Formula

a(n+1) - a(n) is in {2,5,7} for every n.

Mathematica

r = GoldenRatio; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];
Flatten[Position[u, 0]]  (* A283769 *)
Flatten[Position[u, 1]]  (* A283770 *)
Flatten[Position[u, 2]]  (* A283771 *)

Prog

(PARI) r = (1 + 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 = (1 + 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, A283770, A283771.

Sequence in context: A086141 A067883 A325557 * A338352 A117117 A135109

Adjacent sequences: A283766 A283767 A283768 * A283770 A283771 A283772

Keyword

nonn,easy

Author

Clark Kimberling, Mar 18 2017

Status

approved