A185060 Number of Fibonacci integers in the interval [1, 10^n].

10, 88, 534, 2645, 11254, 42735

Offset

1,1

Comments

A Fibonacci integer is an integer in the multiplicative group generated by the Fibonacci numbers. For each fixed epsilon > 0,

exp(C*(log(10^n))^1/2 - (log(10^n))^epsilon) < a(n) < exp(C*(log(10^n))^1/2 + (log(10^n))^(1/6+epsilon)) for x sufficiently large, where C = 2*zeta(2)*sqrt(zeta(3)/(zeta(6)*log((1 + sqrt(5))/2))) = 5.15512.... (Luca, Pomerance, Wagner (2010))

The old entry a(4) = 2681 was the result of an incorrect calculation by Luca, Pomerance and Wagner. - Arkadiusz Wesolowski, Feb 05 2013

Links

Table of n, a(n) for n=1..6.

Florian Luca, Carl Pomerance, and Stephen Wagner, Fibonacci integers (Banff conference in honor of Cam Stewart, May 31, 2010 to June 4, 2010.)

Mathematica

e = 4; (*lst1=the terms of A178762 that are smaller than 10^e*); lst1 = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 61, 89, 107, 199, 211, 233, 281, 421, 521, 1103, 1597, 2161, 2207, 2521, 3001, 3571, 5779, 9349, 9901}; lst2 = {}; q = Times @@ Complement[Prime@Range[10^e], lst1]; Do[If[GCD[q, n] == 1, AppendTo[lst2, n]], {n, 10^e}]; Table[Length@Select[lst2, # <= 10^d &], {d, e}] (* Arkadiusz Wesolowski, Feb 05 2013 *)

Crossrefs

Cf. A178772, A178777.

Sequence in context: A217417 A136864 A099789 * A125398 A273585 A165148

Adjacent sequences: A185057 A185058 A185059 * A185061 A185062 A185063

Keyword

hard,more,nonn

Author

Arkadiusz Wesolowski, Dec 25 2012

Extensions

a(4) corrected by T. D. Noe and Arkadiusz Wesolowski, Feb 05 2013

a(5)-a(6) from Arkadiusz Wesolowski, Feb 06 2013

Status

approved