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A005479 Prime Lucas numbers (cf. A000032).
(Formerly M2627)
10
2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

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).

LINKS

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

MATHEMATICA

Select[LucasL[Range[0, 250]], PrimeQ] (* Harvey P. Dale, Nov 02 2011 *)

CROSSREFS

Cf. A000032, A001606, A113192, A113188.

Sequence in context: A014981 A227885 A096362 * A120856 A138000 A140108

Adjacent sequences:  A005476 A005477 A005478 * A005480 A005481 A005482

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

One further term (from the Knott web site) from Parthasarathy Nambi, Jun 27 2008

STATUS

approved

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Last modified April 19 10:40 EDT 2014. Contains 240747 sequences.