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A190250 Positions of 1 in A190248. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

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 *)

PROG

(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

CROSSREFS

Cf. A190248, A190249, A190251.

Sequence in context: A343177 A085817 A177688 * A047508 A089960 A067888

Adjacent sequences:  A190247 A190248 A190249 * A190251 A190252 A190253

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 06 2011

STATUS

approved

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Last modified May 17 19:39 EDT 2021. Contains 343988 sequences. (Running on oeis4.)