A190250 - OEIS

%I #25 Feb 21 2020 19:29:41

%S 1,4,6,7,9,12,14,15,17,19,20,22,25,27,28,30,33,35,38,40,41,43,46,48,

%T 49,51,54,56,59,61,62,64,67,69,70,72,74,75,77,80,82,83,85,88,90,93,95,

%U 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

%N Positions of 1 in A190248.

%C 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

%H G. C. Greubel, <a href="/A190250/b190250.txt">Table of n, a(n) for n = 1..5500</a>

%H Burghard Herrmann, <a href="/A190250/a190250.pdf">Characterization of some golden ratio sequences</a>

%H Burghard Herrmann, <a href="https://www.fq.math.ca/Papers1/57-5/herrmann.pdf">How integer sequences find their way into areas outside pure mathematics</a>, The Fibonacci Quarterly (2019) Vol. 57, No. 5, 67-71.

%t u = GoldenRatio; v = u^2; w=u^3;

%t f[n_] := Floor[n*u + n*v + n*w] - Floor[n*u] - Floor[n*v] - Floor[n*w]

%t t = Table[f[n], {n, 1, 120}] (* A190248 *)

%t Flatten[Position[t, 0]]      (* A190249 *)

%t Flatten[Position[t, 1]]      (* A190250 *)

%t Flatten[Position[t, 2]]      (* A190251 *)

%o (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

%Y Cf. A190248, A190249, A190251.

%K nonn

%O 1,2

%A _Clark Kimberling_, May 06 2011