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%I #9 Apr 05 2014 13:24:55
%S 37,73,113,149,157,193,269,277,313,353,389,397,457,557,613,673,677,
%T 733,757,877,953,977,997,1069,1093,1153,1213,1237,1453,1657,1753,1873,
%U 1877,1933,1949,1993,2017,2137,2221,2237,2309,2333,2417,2473,2557,2593,2749,2777,2789,2797,2857,2909,2917,3217,3253,3313,3517,3557,3733,4013,4057,4177,4273,4349,4357,4513,4637,4733,4909,4933
%N Prime factors of composite Fibonacci numbers with prime indices (cf. A050937).
%C All numbers in this sequence are congruent to 1 mod 4. - _Max Alekseyev_.
%C If Fibonacci(n) is divisible by a prime p of the form 4k+3 then n is even. To prove this statement it is enough to show that (1+sqrt(5))/(1-sqrt(5)) is never a square modulo such p (which is a straightforward exercise).
%C The n-th prime p is an element of this sequence iff A001602(n) is prime and A051694(n)=A000045(A001602(n))>p. - _Max Alekseyev_
%H Hans Havermann, <a href="/A135952/b135952.txt">Table of n, a(n) for n = 1..5000</a>
%t a = {}; k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], s = FactorInteger[Fibonacci[Prime[n]]]; c = Length[s]; Do[AppendTo[k, s[[m]][[1]]], {m, 1, c}]], {n, 2, 60}]; Union[k]
%Y Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 08 2007
%E Edited, corrected and extended by _Max Alekseyev_, Dec 12 2007
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