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%I #24 Feb 15 2014 15:53:25
%S 10,88,534,2645,11254,42735
%N Number of Fibonacci integers in the interval [1, 10^n].
%C A Fibonacci integer is an integer in the multiplicative group generated by the Fibonacci numbers. For each fixed epsilon > 0,
%C 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))
%C The old entry a(4) = 2681 was the result of an incorrect calculation by Luca, Pomerance and Wagner. - _Arkadiusz Wesolowski_, Feb 05 2013
%H Florian Luca, Carl Pomerance, and Stephen Wagner, <a href="http://www.math.dartmouth.edu/~carlp/fibinttalk.pdf">Fibonacci integers</a> (Banff conference in honor of Cam Stewart, May 31, 2010 to June 4, 2010.)
%t 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 *)
%Y Cf. A178772, A178777.
%K hard,more,nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Dec 25 2012
%E a(4) corrected by _T. D. Noe_ and _Arkadiusz Wesolowski_, Feb 05 2013
%E a(5)-a(6) from _Arkadiusz Wesolowski_, Feb 06 2013
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