A004958 a(n) = ceiling(n*phi^3), where phi is the golden ratio, A001622.

0, 5, 9, 13, 17, 22, 26, 30, 34, 39, 43, 47, 51, 56, 60, 64, 68, 73, 77, 81, 85, 89, 94, 98, 102, 106, 111, 115, 119, 123, 128, 132, 136, 140, 145, 149, 153, 157, 161, 166, 170, 174, 178, 183, 187, 191, 195, 200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This sequence, beginning at 5, gives the positions of 1 in the infinite binary word A188187; complement of A188188. - Clark Kimberling, Mar 23 2011

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001622, A004956, A188014, A188187, A188188.

Programs

Maple

phi:= (sqrt(5)+1)/2:
seq(ceil(2*n*phi)+n, n=0..100); # Robert Israel, Sep 25 2019

Mathematica

r=5^(1/2); k=1;
t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r],{n,1,220}]   (* A188187 *)
Flatten[Position[t,0]]  (* A188188 *)
Flatten[Position[t,1]]  (* A004958 *)
With[{c=GoldenRatio^3},Ceiling[c*Range[0,50]]] (* Harvey P. Dale, Jan 28 2024 *)

Python

from math import isqrt
def A004958(n): return (isqrt(20*n**2)>>1)+(n<<1)+1 if n else 0 # Chai Wah Wu, Aug 17 2022

Formula

a(n) = A004956(2*n) + n. - Robert Israel, Sep 25 2019