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

1, 3, 4, 5, 6, 7, 8, 11, 12, 13, 15, 16, 18, 20, 22, 30, 65, 71, 96, 112, 113, 150, 184, 218, 643, 645, 769, 982, 1059, 1304, 1464, 1649, 1695, 2208, 3776, 3899, 4626, 5236, 5684, 7988, 8700, 9143, 13013, 13681, 14641, 16590, 17433, 18198, 29529, 32870, 37234, 43994, 47150, 50373, 51420, 51929, 52953, 55965, 71398, 82258

Offset: 1

Author

Alexander Adamchuk, Aug 07 2006, Oct 05 2006

Keywords

• nonn

Comments

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.

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,...}.

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,...}.

Crossrefs

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

Cf. A123677, A123678.

Programs

Mathematica

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

Formula

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

Extensions

a(52)-a(60) (from A001606) from Jens Kruse Andersen, Jul 24 2014