Search: id:A135952
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%I A135952
%S A135952 37,73,113,149,157,193,269,277,313,353,389,397,457,557,613,673,677,
%T A135952 733,757,877,953,977,997,1069,1093,1153,1213,1237,1453,1657,1753,
%U A135952 1873,1877,1933,1949,1993,2017,2137,2221,2237,2309,2333,2417,2473,2557,
               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 A135952 Prime factors of composite Fibonacci numbers with prime indices (cf. 
               A050937).
%C A135952 All numbers in this sequence are congruent to 1 mod 4. - Max Alekseyev.
%C A135952 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 A135952 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
%t A135952 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 A135952 Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852.
%Y A135952 Sequence in context: A142100 A093838 A055604 this_sequence A039420 A043243 
               A044023
%Y A135952 Adjacent sequences: A135949 A135950 A135951 this_sequence A135953 A135954 
               A135955
%K A135952 nonn
%O A135952 1,1
%A A135952 Artur Jasinski (grafix(AT)csl.pl), Dec 08 2007
%E A135952 Edited, corrected and extended by Max Alekseyev, Dec 12 2007

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