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A004958 a(n) = ceiling(n*phi^3), where phi is the golden ratio, A001622. 5
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified December 4 07:01 EST 2022. Contains 358544 sequences. (Running on oeis4.)