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%I #8 Sep 08 2022 08:46:07
%S 2,179,239,359,419,487,659,719,883,1013,1019,1439,1459,1499,1559,1723,
%T 1871,1993,2039,2339,2399,2459,2593,2699,2819,2939,3041,3299,3329,
%U 3359,3539,3779,4019,4813,4919,4957,5039,5231,5261,5279,5399,5639,6011,6353,6373
%N Primes p such that gcd(Lucas(p), Mersenne(p)) > 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a>
%e 239 is in the sequence since it is prime and 479 is a prime factor of both Lucas(239) and Mersenne(239) = 2^239 - 1.
%o (Magma) [p: p in PrimesUpTo(6500) | Gcd(Lucas(p),2^p-1) gt 1];
%o (PARI) for(p=2, 6373, if(isprime(p)&&gcd(fibonacci(p-1)+fibonacci(p+1), 2^p-1)>1, print1(p, ", ")));
%Y Supersequence of A230809.
%Y Cf. A000032, A001348.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Mar 21 2014
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