|
Search: id:A001606
|
|
|
| A001606 |
|
Indices of prime Lucas numbers.
(Formerly M0961 N0358)
|
|
+0
14
|
|
| 0, 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, 10691, 12251, 13963, 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
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Some of the larger entries may only correspond to probable primes.
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
|
|
REFERENCES
|
J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260.
H. Dubner, W. Keller, "New Fibonacci and Lucas Primes", Math. Comp. (1998).
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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory and Applications. Chichester: Ellis Horwood Ltd., 1989.
|
|
LINKS
|
D. Broadhurst, Lucas record follows Fibonacci
C. K. Caldwell, The Prime Glossary, Lucas prime
B. Kelly, Factorizations of Lucas numbers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Integer Sequence Primes
|
|
CROSSREFS
|
Cf. A000032, A000204, A005479.
A080327 shows the n for which Lucas(n) and Fibonacci(n) are both prime.
Sequence in context: A022559 A049781 A076697 this_sequence A014554 A114147 A025516
Adjacent sequences: A001603 A001604 A001605 this_sequence A001607 A001608 A001609
|
|
KEYWORD
|
nonn,hard,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
4 more terms from D.Broadhurst(AT)open.ac.uk, Jun 08 2001
More terms from T. D. Noe (noe(AT)sspectra.com), Feb 15 2003 and Mar 04 2003; see link to The Prime Glossary.
387433, 443609, 532277 and 574219 found by R. Lifchitz, contributed by Eric Weisstein (eric(AT)weisstein.com), Nov 29, 2005
616787, 631181, 637751, 651821, 692147 found by Henri Lifchitz, circa Oct 01 2008, contributed by Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 28 2008
|
|
|
Search completed in 0.002 seconds
|
