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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
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
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
KEYWORD
nonn
STATUS
approved