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

0,2

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A291180 A057948 A314682 * A190887 A314683 A184479

Adjacent sequences: A004955 A004956 A004957 * A004959 A004960 A004961

Keyword

nonn

Author

N. J. A. Sloane

Status

approved