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A120561 Numbers n such that Lucas(prime(n)) is prime, where Lucas = A000032. 2

%I

%S 1,3,4,5,6,7,8,11,12,13,15,16,18,20,22,30,65,71,96,112,113,150,184,

%T 218,643,645,769,982,1059,1304,1464,1649,1695,2208,3776,3899,4626,

%U 5236,5684,7988,8700,9143,13013,13681,14641,16590,17433,18198,29529,32870,37234,43994,47150,50373,51420,51929,52953,55965,71398,82258

%N Numbers n such that Lucas(prime(n)) is prime, where Lucas = A000032.

%C 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 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,...}.

%C 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.

%C 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,...}.

%F a(n) = PrimePi(A001606(n+4)) for n>5.

%t Select[ Range[300], PrimeQ[ Fibonacci[ Prime[ # ] - 1 ] + Fibonacci[ Prime[ # ] + 1 ]] & ]

%Y Cf. A000032, A119984. Cf. A001606 - Indices of prime Lucas numbers.

%Y Cf. A123677, A123678.

%K nonn

%O 1,2

%A _Alexander Adamchuk_, Aug 07 2006, Oct 05 2006

%E a(52)-a(60) (from A001606) from _Jens Kruse Andersen_, Jul 24 2014

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Last modified August 6 12:33 EDT 2020. Contains 336246 sequences. (Running on oeis4.)