Search: id:A001606
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%I A001606 M0961 N0358
%S A001606 0,2,4,5,7,8,11,13,16,17,19,31,37,41,47,53,61,71,79,113,313,353,503,
%T A001606 613,617,863,1097,1361,4787,4793,5851,7741,8467,10691,12251,13963,
%U A001606 14449,19469,35449,36779,44507,51169,56003,81671,89849,94823,140057,148091,
               159521,183089,193201,202667,344293,387433,443609,532277,574219,616787,
               631181,637751,651821,692147
%N A001606 Indices of prime Lucas numbers.
%C A001606 Some of the larger entries may only correspond to probable primes.
%C A001606 Since (as noted under A000032) L(n) divides L(mn) whenever m is odd, 
               L(n) cannot be prime unless n is itself prime, or else n contains 
               no odd divisor, i.e. is a power of 2. Potential divisors of L(n) 
               must satisfy certain linear forms dependent upon the parity of n, 
               as shown in Vajda (1989), p. 82 (with a slight typographical error 
               in the proof). - John Blythe Dobson (j.dobson(AT)uwinnipeg.ca), Oct 
               22 2007
%D A001606 J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci 
               and Lucas factorizations, Math. Comp. 50 (1988), 251-260.
%D A001606 H. Dubner, W. Keller, "New Fibonacci and Lucas Primes", Math. Comp. (1998).
%D A001606 Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas 
               n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 
               05.4.4.
%D A001606 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001606 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001606 S. Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory 
               and Applications. Chichester: Ellis Horwood Ltd., 1989.
%H A001606 D. Broadhurst, <a href="http://groups.yahoo.com/group/primenumbers/message/
               1003">Lucas record follows Fibonacci</a>
%H A001606 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php?sort=LucasPrime">Lucas prime</a>
%H A001606 B. Kelly, <a href="http://home.att.net/~blair.kelly/mathematics/fibonacci/
               lucas.txt">Factorizations of Lucas numbers</a>
%H A001606 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LucasNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A001606 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IntegerSequencePrimes.html">Integer Sequence Primes</a>
%Y A001606 Cf. A000032, A000204, A005479.
%Y A001606 A080327 shows the n for which Lucas(n) and Fibonacci(n) are both prime.
%Y A001606 Sequence in context: A022559 A049781 A076697 this_sequence A014554 A114147 
               A025516
%Y A001606 Adjacent sequences: A001603 A001604 A001605 this_sequence A001607 A001608 
               A001609
%K A001606 nonn,hard,nice
%O A001606 1,2
%A A001606 N. J. A. Sloane (njas(AT)research.att.com).
%E A001606 4 more terms from D.Broadhurst(AT)open.ac.uk, Jun 08 2001
%E A001606 More terms from T. D. Noe (noe(AT)sspectra.com), Feb 15 2003 and Mar 
               04 2003; see link to The Prime Glossary.
%E A001606 387433, 443609, 532277 and 574219 found by R. Lifchitz, contributed by 
               Eric Weisstein (eric(AT)weisstein.com), Nov 29, 2005
%E A001606 616787, 631181, 637751, 651821, 692147 found by Henri Lifchitz, circa 
               Oct 01 2008, contributed by Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Nov 28 2008

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