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A238749
Exponents of third Mersenne prime pair: numbers n such that 2^n - 5 and 5*2^n - 1 are both prime.
1
4, 8, 10, 12, 18, 32
OFFSET
1,1
COMMENTS
a(7) > 350028.
Intersection of A059608 and A001770.
Exponents of Mersenne prime pairs {2^n - (2k + 1), (2k + 1)*2^n - 1}:
for k = 0: 2, 3, 5, 7, 13, 17, ... Intersection of A000043 and A000043
for k = 1: 3, 4, 6, 94, ... Intersection of A050414 and A002235
for k = 2: 4, 8, 10, 12, 18, 32, ... Intersection of A059608 and A001770
for k = 3: Intersection of A059609 and A001771
for k = 4: 21, ... Intersection of A059610 and A002236
for k = 5: Intersection of A096817 and A001772
for k = 6: Intersection of A096818 and A001773
for k = 7: 5, 10, 14, ... Intersection of A059612 and A002237
for k = 8: 6, 16, 20, 36, ... Intersection of A059611 and A001774
for k = 9: 5, 21, ... Intersection of A096819 and A001775
for k = 10: 7, 13, ... Intersection of A096820 and A002238
for k = 11: 6, 8, 12, ...
for k = 12: 9, ...
for k = 13: 5, 8, 10, ...
for k = 14:
EXAMPLE
a(1) = 4 because 2^4 - 5 = 11 and 5*2^4 - 1 = 79 are both primes.
MATHEMATICA
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 *)
Select[Range[1000], PrimeQ[2^# - 5] && PrimeQ[5 2^# - 1] &] (* Vincenzo Librandi, May 17 2015 *)
PROG
(PARI) isok(n) = isprime(2^n - 5) && isprime(5*2^n - 1); \\ Michel Marcus, Mar 04 2014
(Magma) [n: n in [0..100] | IsPrime(2^n-5) and IsPrime(5*2^n-1)]; // Vincenzo Librandi, May 17 2015
KEYWORD
nonn,more
AUTHOR
STATUS
approved