A283774 Numbers k such that U(k) == 2 mod 3, where U = A001950 = upper Wythoff sequence.

1, 2, 8, 9, 10, 16, 17, 18, 24, 25, 26, 32, 33, 34, 40, 41, 48, 49, 55, 56, 57, 63, 64, 65, 71, 72, 73, 79, 80, 81, 87, 88, 89, 95, 96, 103, 104, 110, 111, 112, 118, 119, 120, 126, 127, 128, 134, 135, 136, 142, 143, 150, 151, 158, 159, 165, 166, 167, 173

Offset

1,2

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==2, print1(n, ", "))) \\ Indranil Ghosh, Mar 21 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==2] # Indranil Ghosh, Mar 21 2017

Crossrefs

Cf. A000201, A001622, A283772, A283774.

Sequence in context: A318175 A318182 A047469 * A037456 A277857 A360427

Adjacent sequences: A283771 A283772 A283773 * A283775 A283776 A283777

Keyword

nonn,easy

Author

Clark Kimberling, Mar 19 2017

Status

approved