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A005479
Prime Lucas numbers (cf. A000032).
(Formerly M2627)
17
2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521
OFFSET
1,1
COMMENTS
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
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, Section A3.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260.
Harvey P. Dale and others, A005479 and A153867, SeqFan list, Apr 24 2014.
Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
Eric Weisstein's World of Mathematics, Lucas Number
MATHEMATICA
Select[LucasL[Range[0, 250]], PrimeQ] (* Harvey P. Dale, Nov 02 2011 *)
CROSSREFS
KEYWORD
nonn,nice
EXTENSIONS
One further term (from the Knott web site) from Parthasarathy Nambi, Jun 27 2008
STATUS
approved