

A005479


Prime Lucas numbers (cf. A000032).
(Formerly M2627)


12



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

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
For n>2 also: Primes which are the sum of four consecutive Fibonacci numbers, a(n) = A153867(n2), 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

J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251260.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..28
Harvey P. Dale and others, A005479 and A153867, SeqFan list, Apr 24 2014.
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 nstep and Lucas nstep 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



