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A080050
Primes p such that 2^p-1 and the p-th Fibonacci number have a common factor. Prime terms of A074776.
4
11, 8501, 10867, 13109, 14633, 15401, 17657, 19211, 19541, 22481, 24359, 25243, 26111, 29411, 30851, 34961, 36007, 42443, 43331, 45523, 46187, 46601, 47591, 50411, 57251, 58027, 61001, 62921, 63131, 64123, 70639, 74293, 76919, 78941
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A074776 and all multiples k*p of this sequence are in A074776, i.e., they satisfy gcd(2^(k*p)-1, Fibonacci(k*p)) > 1. This was proved by Anthony Mendes.
LINKS
EXAMPLE
89 divides both 2^11-1=2047 and Fibonacci(11)=89, so 11 is in the sequence.
MATHEMATICA
Select[Prime[Range[8000]], GCD[2^#-1, Fibonacci[#]]>1&] (* Harvey P. Dale, Mar 16 2020 *)
PROG
(PARI) forprime(p=1, 10^5, if(gcd(2^p-1, fibonacci(p))>1, print(p))).
CROSSREFS
Common factors are in A080051.
Sequence in context: A214183 A214234 A320984 * A067254 A099806 A227063
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jan 22 2003
STATUS
approved