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Search: id:A120561
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| A120561 |
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Numbers n such that Lucas[ Prime[n] ] is prime, where Lucas[k] = A000032[k]. |
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3
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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,...}. 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,...}.
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MATHEMATICA
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Select[ Range[300], PrimeQ[ Fibonacci[ Prime[ # ] - 1 ] + Fibonacci[ Prime[ # ] + 1 ]] & ]
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CROSSREFS
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Cf. A000032, A119984. Cf. A001606 - Indices of prime Lucas numbers.
Cf. A123677, A123678.
Adjacent sequences: A120558 A120559 A120560 this_sequence A120562 A120563 A120564
Sequence in context: A089358 A001272 A047563 this_sequence A051016 A044951 A138308
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 07 2006, Oct 05 2006
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