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A005479
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Prime Lucas numbers (cf. A000032).
(Formerly M2627)
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10
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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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Also primes of the form 2*F(k) + F(k+1) or F(k) + 3*F(k+1), where F(k) is a Fibonacci number. - Giovanni Teofilatto, Jun 06 2004
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
With reference to the first comment, primes of the form F(k)+F(k+2). - Paolo P. Lava, Jul 19 2012
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REFERENCES
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J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260.
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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Table of n, a(n) for n=1..21.
Blair Kelly, Factorizations of Lucas numbers
Ron Knott, The First 200 Lucas numbers and their factors.
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
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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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Cf. A000032, A001606, A113192, A113188.
Sequence in context: A112840 A014981 A096362 * A120856 A138000 A140108
Adjacent sequences: A005476 A005477 A005478 * A005480 A005481 A005482
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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One further term (from the Knott web site) from Parthasarathy Nambi, Jun 27 2008
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STATUS
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approved
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