cp's OEIS Frontend

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

%I A004958 #41 Jun 01 2025 03:33:49
%S A004958 0,5,9,13,17,22,26,30,34,39,43,47,51,56,60,64,68,73,77,81,85,89,94,98,
%T A004958 102,106,111,115,119,123,128,132,136,140,145,149,153,157,161,166,170,
%U A004958 174,178,183,187,191,195,200
%N A004958 a(n) = ceiling(n*phi^3), where phi is the golden ratio, A001622.
%C A004958 This sequence, beginning at 5, gives the positions of 1 in the infinite binary word A188187; complement of A188188. - _Clark Kimberling_, Mar 23 2011
%H A004958 Ivan Panchenko, <a href="/A004958/b004958.txt">Table of n, a(n) for n = 0..1000</a>
%F A004958 a(n) = A004956(2*n) + n. - _Robert Israel_, Sep 25 2019
%p A004958 phi:= (sqrt(5)+1)/2:
%p A004958 seq(ceil(2*n*phi)+n, n=0..100); # _Robert Israel_, Sep 25 2019
%t A004958 r=5^(1/2); k=1;
%t A004958 t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r],{n,1,220}]   (* A188187 *)
%t A004958 Flatten[Position[t,0]]  (* A188188 *)
%t A004958 Flatten[Position[t,1]]  (* A004958 *)
%t A004958 With[{c=GoldenRatio^3},Ceiling[c*Range[0,50]]] (* _Harvey P. Dale_, Jan 28 2024 *)
%o A004958 (Python)
%o A004958 from math import isqrt
%o A004958 def A004958(n): return (isqrt(20*n**2)>>1)+(n<<1)+1 if n else 0 # _Chai Wah Wu_, Aug 17 2022
%Y A004958 Cf. A001622, A004956, A188014, A188187, A188188.
%K A004958 nonn
%O A004958 0,2
%A A004958 _N. J. A. Sloane_