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Search: id:A080050
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| A080050 |
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Primes p such that 2^p-1 and the p-th Fibonacci number have a common factor. Prime members of A074776. |
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+0
4
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| 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
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OFFSET
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1,1
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COMMENT
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The sequence is a subset of A074776 and all multiples k*p of this sequence are in A074776, i.e. they satisfy gcd(2^(kp)-1,fibonacci(kp)) > 1. This was proved by Anthony Mendes.
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EXAMPLE
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Example: 89 divides both 2^11-1=2047 and F(11)=89, so 11 is in the sequence.
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PROGRAM
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(PARI) forprime(p=1, 10^5, if(gcd(2^p-1, fibonacci(p))>1, print(p))).
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CROSSREFS
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Cf. A074776, A079506, A079670. Common factors are in A080051.
Sequence in context: A023334 A068730 A167068 this_sequence A067254 A099806 A050647
Adjacent sequences: A080047 A080048 A080049 this_sequence A080051 A080052 A080053
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 22 2003
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