Search: id:A120561
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%I A120561
%S A120561 1,3,4,5,6,7,8,11,12,13,15,16,18,20,22,30,65,71,96,112,113,150,184,218,
%T A120561 643,645,769,982,1059,1304,1464,1649,1695,2208,3776,3899,4626,5236,5684,
%U A120561 7988,8700,9143,13013,13681,14641,16590,17433,18198,29529,32870,37234
%N A120561 Numbers n such that Lucas[ Prime[n] ] is prime, where Lucas[k] = A000032[k].
%C A120561 All prime Lucas numbers A000032[n] have indices that are prime, zero 
               or a power of 2. It is a conjecture that all indices of prime Lucas 
               numbers are prime, except n = 0, 4, 8, 16.
%C A120561 Indices of prime Lucas numbers are listed in A001606[n] = {0,2,4,5,7,
               8,11,13,16,17,19,31,37,41,47,53,61,...}. a(n) = PrimePi[ A001606[n+4] 
               ] for n>5. Primes in a(n) are listed in A123677[n] = {3,5,7,11,13,
               71,113,643,769,13681,...} Primes p such that Lucas[Prime[p]] is prime. 
               Numbers n such that Lucas[Prime[Prime[n]]] is prime are listed in 
               A123678[n] = PrimePi[A123677[n]] = {2,3,4,5,6,20,30,117,136,1616,
               ...}.
%t A120561 Select[ Range[300], PrimeQ[ Fibonacci[ Prime[ # ] - 1 ] + Fibonacci[ 
               Prime[ # ] + 1 ]] & ]
%Y A120561 Cf. A000032, A119984. Cf. A001606 - Indices of prime Lucas numbers.
%Y A120561 Cf. A123677, A123678.
%Y A120561 Sequence in context: A089358 A001272 A047563 this_sequence A051016 A044951 
               A138308
%Y A120561 Adjacent sequences: A120558 A120559 A120560 this_sequence A120562 A120563 
               A120564
%K A120561 nonn
%O A120561 1,2
%A A120561 Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 07 2006, Oct 05 2006

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