A126612 a(n) is the least K such that K*6*M(n) - 1 and K*6*M(n) + 1 are twin primes, where M(n) = n-th Mersenne prime.

1, 1, 7, 24, 12, 52, 24, 39, 252, 112, 371, 184, 5772, 44649, 61939, 151505, 64125, 533040, 407635, 273249, 3901012, 718187, 3527063, 9522163, 23128315, 20121642, 337342290, 388787370

Offset

1,3

Links

Table of n, a(n) for n=1..28.

R. Gerbicz, PolySieve program at UTM Prime Pages.

Mersenneforum, k.Mp +/- 1 discussion thread.

Example

7*6*(2^5-1)-1=1301 prime, 1301 and 1303 twin primes so K(3)=7 as M(3)=2^5-1.

Mathematica

Array[Block[{k = 1, m = 2^MersennePrimeExponent@ # - 1}, While[! AllTrue[6 k m + {-1, 1}, PrimeQ], k++]; k] &, 14] (* Michael De Vlieger, Dec 22 2019 *)

Prog

(PARI) forprime(p=2, 607, if(isprime(Mp=2^p-1), forstep(k=6, 10^9, 6, if(isprime(k*Mp-1), if(isprime(k*Mp+1), print1(k/6", "); break))))) \\ Serge Batalov, Dec 22 2019

Crossrefs

Cf. A000043, A000668.

Sequence in context: A012482 A124985 A349078 * A196113 A286506 A286406

Adjacent sequences: A126609 A126610 A126611 * A126613 A126614 A126615

Keyword

nonn,more

Author

Pierre CAMI, Feb 08 2007

Extensions

Missing term 44649 and a(26-28) from Serge Batalov, Dec 21 2019

Status

approved