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A005479
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Prime Lucas numbers (cf. A000032).
(Formerly M2627)
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14
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2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521
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OFFSET
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1,1
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COMMENTS
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It appears that a(n) is the intersection ( or a subset of the intersection ) of A113192[n], Primes that are the difference of two Lucas numbers and A113188[n], Primes that are the difference of two Fibonacci numbers, excluding A113192[1] = A113188[1] = 2. - Alexander Adamchuk, Aug 06 2006
For n>2 also: Primes which are the sum of four consecutive Fibonacci numbers, a(n) = A153867(n-2), cf. link to SeqFan list (Apr. 2014). - M. F. Hasler, Apr 24 2014
Conjectures: 7, 47 and 2207 are the only a(n) mod 10 = 7. They are also the only a(n) values where the Lucas index is not a prime. See A001606 for the Lucas index values of these primes. See A266587 for the divisibility of Lucas numbers by powers of primes. - Richard R. Forberg, Mar 24 2016
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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Select[LucasL[Range[0, 250]], PrimeQ] (* Harvey P. Dale, Nov 02 2011 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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