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Search: id:A005479
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| 2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also primes of the form 2*F(n) + F(n+1) or F(n) + 3*F(n), where F(n) 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 (alex(AT)kolmogorov.com), Aug 06 2006
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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.
Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
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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B. Kelly, Factorizations of Lucas numbers
Ron Knott, The First 200 Lucas numbers and their factors.
Eric Weisstein's World of Mathematics, Lucas Number
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MATHEMATICA
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lst={}; b=2; c=1; AppendTo[lst, b]; Do[b=b+c; If[PrimeQ[b], AppendTo[lst, b]]; c=b+c; If[PrimeQ[c], AppendTo[lst, c]], {n, 1, 15^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 21 2008]
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CROSSREFS
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Cf. A000032, A001606, A113192, A113188.
Sequence in context: A112840 A014981 A096362 this_sequence A120856 A138000 A034295
Adjacent sequences: A005476 A005477 A005478 this_sequence 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 (njas(AT)research.att.com).
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EXTENSIONS
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One further term (from the Knott web site) from Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Jun 27 2008
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