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Primes p such that 2^p-1 and the p-th Fibonacci number have a common factor. Prime terms of A074776.
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%I #17 May 08 2021 23:22:52

%S 11,8501,10867,13109,14633,15401,17657,19211,19541,22481,24359,25243,

%T 26111,29411,30851,34961,36007,42443,43331,45523,46187,46601,47591,

%U 50411,57251,58027,61001,62921,63131,64123,70639,74293,76919,78941

%N Primes p such that 2^p-1 and the p-th Fibonacci number have a common factor. Prime terms of A074776.

%C 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.

%H Amiram Eldar, <a href="/A080050/b080050.txt">Table of n, a(n) for n = 1..1000</a>

%e 89 divides both 2^11-1=2047 and Fibonacci(11)=89, so 11 is in the sequence.

%t Select[Prime[Range[8000]],GCD[2^#-1,Fibonacci[#]]>1&] (* _Harvey P. Dale_, Mar 16 2020 *)

%o (PARI) forprime(p=1,10^5,if(gcd(2^p-1,fibonacci(p))>1,print(p))).

%Y Cf. A000045, A030426, A074776, A079506, A079670.

%Y Common factors are in A080051.

%K nonn

%O 1,1

%A _Ralf Stephan_, Jan 22 2003