A283747 a(n) = least m such that 1/2^(n+1) < f(m) < 1/2^n, where f(m) = fractional part of m*(golden ratio).

1, 4, 2, 5, 13, 68, 34, 89, 466, 233, 610, 1597, 8362, 4181, 10946, 28657, 150050, 75025, 196418, 1028458, 514229, 1346269, 3524578, 18454930, 9227465, 24157817, 126491972, 63245986, 165580141, 433494437, 2269806340, 1134903170, 2971215073, 15557484098

Offset

0,2

Comments

This is column 1 of A283740; |a(n+1) - a(n)| is a Fibonacci number for n >= 1.

Links

Table of n, a(n) for n=0..33.

Mathematica

g = GoldenRatio; z = 50000; t = Table[N[FractionalPart[n*g]], {n, 1, z}];
r[k_] := Select[Range[z], 1/2^(k + 1) < t[[#]] < 1/2^k &, 1];
Flatten[Table[r[k], {k, 0, 200}]]  (* A283747 *)

Crossrefs

Cf. A000045, A001622, A283740, A283748.

Sequence in context: A200608 A163358 A121709 * A180109 A019170 A107504

Adjacent sequences: A283744 A283745 A283746 * A283748 A283749 A283750

Keyword

nonn,easy

Author

Clark Kimberling, Mar 17 2017

Extensions

Offset and a(16) corrected and a(17)-a(33) added by Jon E. Schoenfield, Apr 02 2017

Status

approved