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%I M2627 #55 Feb 16 2024 10:08:55
%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 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 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 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 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 Harvey P. Dale and others, <a href="http://list.seqfan.eu/oldermail/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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