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 A074714 Primes that divide Fibonacci number F(2^k) for some k. 0
 3, 7, 47, 127, 1087, 2207, 4481, 21503, 34303, 119809, 524287, 65241089, 167772161, 1811939329, 2147483647, 3758096383, 16074670081, 73327699969, 186812208641, 206158430209, 2142130536449, 2878401282049, 5703716569087, 15868293545983, 274367023939583 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Going out to Fibonacci(2^9) gives the additional terms 73327699969, 186812208641, 4698167634523379875583, 125960894984050328038716298487435392001. - Lambert Klasen (lambert.klasen(AT)gmx.de), Jan 08 2005 21503 is a factor of Fibonacci(2^10). 524287 is a factor of Fibonacci(2^19). 65241089 is a factor of Fibonacci(2^13). -Donovan Johnson, Feb 21 2008 From the divisibility properties of Fibonacci numbers, if a prime divides F(2^k), then it divides F(2^m) for all m >= k. The smallest value of k for these primes is 2, 3, 4, 7, 6, 5, 6, 10, 9, 8, 19, 13, 24, 23, 31, 29, 20, 9, 7, 32, 15, 16, 36, 29, 24. Every integer > 1 will occur as k because every Fibonacci other than F(0), F(1), F(6), and F(12) has a primitive prime factor. LINKS EXAMPLE F(2^5)= 3*7*47*2207 hence 3,7,47,2207 are in the sequence. PROG (PARI) forprime(p=3, 10^5, if(lift((matrix(2, 2, i, j, Mod(i+j<4, p))^(2^(valuation(p*p-1, 2)-1)))[1, 2])==0, print1(p", "))) - Robert Gerbicz, Dec 17 2010 CROSSREFS Sequence in context: A129518 A007670 A263806 * A064457 A318087 A005650 Adjacent sequences:  A074711 A074712 A074713 * A074715 A074716 A074717 KEYWORD nonn AUTHOR Benoit Cloitre, Sep 04 2002 EXTENSIONS 3 more terms from Donovan Johnson, Feb 21 2008 a(13)-a(25) from Robert Gerbicz, Dec 17 2010 STATUS approved

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Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)