cp's OEIS Frontend

A238749 Exponents of third Mersenne prime pair: numbers n such that 2^n - 5 and 5*2^n - 1 are both prime.

%I A238749 #36 Sep 08 2022 08:46:07
%S A238749 4,8,10,12,18,32
%N A238749 Exponents of third Mersenne prime pair: numbers n such that 2^n - 5 and 5*2^n - 1 are both prime.
%C A238749 a(7) > 350028.
%C A238749 Intersection of A059608 and A001770.
%C A238749 Exponents of Mersenne prime pairs {2^n - (2k + 1), (2k + 1)*2^n - 1}:
%C A238749 for k = 0: 2, 3, 5, 7, 13, 17, ...   Intersection of A000043 and A000043
%C A238749 for k = 1: 3, 4, 6, 94, ...          Intersection of A050414 and A002235
%C A238749 for k = 2: 4, 8, 10, 12, 18, 32, ... Intersection of A059608 and A001770
%C A238749 for k = 3:                           Intersection of A059609 and A001771
%C A238749 for k = 4: 21, ...                   Intersection of A059610 and A002236
%C A238749 for k = 5:                           Intersection of A096817 and A001772
%C A238749 for k = 6:                           Intersection of A096818 and A001773
%C A238749 for k = 7: 5, 10, 14, ...            Intersection of A059612 and A002237
%C A238749 for k = 8: 6, 16, 20, 36, ...        Intersection of A059611 and A001774
%C A238749 for k = 9: 5, 21, ...                Intersection of A096819 and A001775
%C A238749 for k = 10: 7, 13, ...               Intersection of A096820 and A002238
%C A238749 for k = 11: 6, 8, 12, ...
%C A238749 for k = 12: 9, ...
%C A238749 for k = 13: 5, 8, 10, ...
%C A238749 for k = 14:
%e A238749 a(1) = 4 because 2^4 - 5 = 11 and 5*2^4 - 1 = 79 are both primes.
%t A238749 fQ[n_] := PrimeQ[2^n - 5] && PrimeQ[5*2^n - 1]; k = 1; While[ k < 15001, If[fQ@ k, Print@ k]; k++] (* _Robert G. Wilson v_, Mar 05 2014 *)
%t A238749 Select[Range[1000], PrimeQ[2^# - 5] && PrimeQ[5 2^# - 1] &] (* _Vincenzo Librandi_, May 17 2015 *)
%o A238749 (PARI) isok(n) = isprime(2^n - 5) && isprime(5*2^n - 1); \\ _Michel Marcus_, Mar 04 2014
%o A238749 (Magma) [n: n in [0..100] | IsPrime(2^n-5) and IsPrime(5*2^n-1)]; // _Vincenzo Librandi_, May 17 2015
%Y A238749 Cf. A000043, A001770, A059608, A237422, A238694, A238251, A238751, A238797.
%K A238749 nonn,more
%O A238749 1,1
%A A238749 _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Mar 04 2014