A190250 Positions of 1 in A190248.

1, 4, 6, 7, 9, 12, 14, 15, 17, 19, 20, 22, 25, 27, 28, 30, 33, 35, 38, 40, 41, 43, 46, 48, 49, 51, 54, 56, 59, 61, 62, 64, 67, 69, 70, 72, 74, 75, 77, 80, 82, 83, 85, 88, 90, 93, 95, 96, 98, 101, 103, 104, 106, 108, 109, 111, 114, 116, 117, 119, 122, 124, 125, 127, 129, 130, 132, 135, 137, 138, 140, 143, 145, 148, 150, 151, 153, 156, 158, 159, 161

Offset: 1

Author

Clark Kimberling, May 06 2011

Keywords

• nonn

Comments

Numbers n such that 1/4 < {n*phi} < 3/4, where phi is the golden ratio (1+sqrt(5))/2 and { } denotes fractional part. - Burghard Herrmann, Nov 14 2017

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5500
• Burghard Herrmann, Characterization of some golden ratio sequences
• Burghard Herrmann, How integer sequences find their way into areas outside pure mathematics, The Fibonacci Quarterly (2019) Vol. 57, No. 5, 67-71.

Crossrefs

Cf. A190248, A190249, A190251.

Programs

Mathematica

u = GoldenRatio; v = u^2; w=u^3;
f[n_] := Floor[n*u + n*v + n*w] - Floor[n*u] - Floor[n*v] - Floor[n*w]
t = Table[f[n], {n, 1, 120}] (* A190248 *)
Flatten[Position[t, 0]]      (* A190249 *)
Flatten[Position[t, 1]]      (* A190250 *)
Flatten[Position[t, 2]]      (* A190251 *)

PARI

isok(n) = my(u=(1+sqrt(5))/2); floor(2*n+4*n*u)-floor(n*u)-floor(n+n*u)-floor(n+2*n*u) == 1; \\ Michel Marcus, Nov 14 2017