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.
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
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