A283773 Numbers k such that U(k) = 1 mod 3, where U = A001950 = upper Wythoff sequence.

3, 4, 5, 11, 12, 13, 19, 20, 27, 28, 35, 36, 42, 43, 44, 50, 51, 52, 58, 59, 60, 66, 67, 68, 74, 75, 82, 83, 90, 91, 97, 98, 99, 105, 106, 107, 113, 114, 115, 121, 122, 123, 129, 130, 137, 138, 144, 145, 146, 152, 153, 154, 160, 161, 162, 168, 169, 170, 176

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==1, 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==1] # Indranil Ghosh, Mar 19 2017

Crossrefs

Cf. A000201, A001622, A283772, A283774.

Sequence in context: A128920 A006288 A047598 * A214256 A067532 A276470

Adjacent sequences: A283770 A283771 A283772 * A283774 A283775 A283776

Keyword

nonn,easy

Author

Clark Kimberling, Mar 18 2017

Status

approved