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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 (list; graph; refs; listen; history; text; internal format)
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:

LINKS

Table of n, a(n) for n=1..6.

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

CROSSREFS

Cf. A000043, A001770, A059608, A237422, A238694, A238251, A238751, A238797.

Sequence in context: A310981 A310982 A310983 * A310984 A295265 A172153

Adjacent sequences:  A238746 A238747 A238748 * A238750 A238751 A238752

KEYWORD

nonn,more

AUTHOR

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 04 2014

STATUS

approved

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Last modified November 16 22:43 EST 2018. Contains 317275 sequences. (Running on oeis4.)