A283770 Numbers k such that L(k) = 1 mod 3, where L = A000201 = lower Wythoff sequence.

1, 3, 10, 12, 14, 16, 23, 25, 27, 29, 34, 36, 38, 40, 42, 47, 49, 51, 53, 55, 60, 62, 64, 66, 73, 75, 77, 79, 86, 88, 90, 92, 99, 101, 103, 105, 112, 114, 116, 118, 123, 125, 127, 129, 131, 136, 138, 140, 142, 144, 149, 151, 153, 155, 162, 164, 166, 168, 175

Offset

1,2

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

Crossrefs

Cf. A000201, A001622, A283769, A283771.

Sequence in context: A212993 A272968 A020681 * A088338 A020890 A343892

Adjacent sequences: A283767 A283768 A283769 * A283771 A283772 A283773

Keyword

nonn,easy

Author

Clark Kimberling, Mar 18 2017

Status

approved