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 A005479 Prime Lucas numbers (cf. A000032). (Formerly M2627) 14

%I M2627

%S 2,3,7,11,29,47,199,521,2207,3571,9349,3010349,54018521,370248451,

%T 6643838879,119218851371,5600748293801,688846502588399,

%U 32361122672259149,412670427844921037470771,258899611203303418721656157249445530046830073044201152332257717521

%N Prime Lucas numbers (cf. A000032).

%C 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

%C 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 With reference to the first comment, primes of the form F(k)+F(k+2). - _Paolo P. Lava_, Jul 19 2012

%C 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 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 J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A005479/b005479.txt">Table of n, a(n) for n = 1..28</a>

%H Harvey P. Dale and others, <a href="http://list.seqfan.eu/pipermail/seqfan/2014-April/012877.html">A005479 and A153867</a>, SeqFan list, Apr 24 2014.

%H Blair Kelly, <a href="http://mersennus.net/fibonacci//lucas.txt">Factorizations of Lucas numbers</a>

%H 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>

%t Select[LucasL[Range[0,250]], PrimeQ] (* _Harvey P. Dale_, Nov 02 2011 *)

%Y Cf. A000032, A001606, A113192, A113188.

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_.

%E One further term (from the Knott web site) from _Parthasarathy Nambi_, Jun 27 2008

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)