%I A005479 M2627 #67 Oct 04 2026 13:21:49
%S A005479 2,3,7,11,29,47,199,521,2207,3571,9349,3010349,54018521,370248451,
%T A005479 6643838879,119218851371,5600748293801,688846502588399,
%U A005479 32361122672259149,412670427844921037470771,258899611203303418721656157249445530046830073044201152332257717521
%N A005479 Prime Lucas numbers (cf. A000032).
%C A005479 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
%C A005479 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
%C A005479 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
%D A005479 R. K. Guy, Unsolved Problems in Number Theory, Section A3.
%D A005479 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005479 T. D. Noe, <a href="/A005479/b005479.txt">Table of n, a(n) for n = 1..28</a>
%H A005479 J. Brillhart, P. L. Montgomery and R. D. Silverman, <a href="https://doi.org/10.1090/S0025-5718-1988-0917832-6">Tables of Fibonacci and Lucas factorizations</a>, Math. Comp. 50 (1988), 251-260.
%H A005479 Harvey P. Dale and others, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-April/012877.html">A005479 and A153867</a>, SeqFan list, Apr 24 2014.
%H A005479 Blair Kelly, <a href="http://mersennus.net/fibonacci//lucas.txt">Factorizations of Lucas numbers</a>
%H A005479 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/lucas200.html">The First 200 Lucas numbers and their factors</a>.
%H A005479 Tony D. Noe and Jonathan Vos Post, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Noe/noe5.html">Primes in Fibonacci n-step and Lucas n-step Sequences</a>, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
%H A005479 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>.
%H A005479 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasPrime.html">Lucas Prime</a>.
%t A005479 Select[LucasL[Range[0,250]], PrimeQ] (* _Harvey P. Dale_, Nov 02 2011 *)
%Y A005479 Cf. A000032, A001606, A113192, A113188.
%K A005479 nonn,nice,changed
%O A005479 1,1
%A A005479 _N. J. A. Sloane_
%E A005479 One further term (from the Knott web site) from _Parthasarathy Nambi_, Jun 27 2008