A143385 -id:A143385 - cp's OEIS frontend

A139426 Smallest number k such that M(n)^2+k*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

1, 5, 1, 5, 11, 11, 17, 19, 23, 97, 127, 145, 167, 269, 767, 479, 3307, 1453, 18007, 2357, 599, 17669, 5527, 3191, 3251, 70249, 147773, 39637

Offset: 1

Pierre CAMI, Apr 21 2008

All primes certified using openpfgw_v12 from primeform group.

			3*3+1*3-1=11 prime 3=M(1)=2^2-1 so k(1)=1;
7*7+5*7-1=83 prime 7=M(2)=2^3-1 so k(2)=5;
31*31+1*31-1=991 prime 31=M(3)=2^5-1 so k(3)=1.

Cf. A000668, A139424, A139425, A139427, A139428, A139429, A139430, A139421, A143385.

A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; k = 1;
While[! PrimeQ[m2 + k*m - 1], k++]; k, {n, 15}] (* Robert Price, Apr 17 2019 *)

3 more terms. - Pierre CAMI, Aug 11 2008

A143384 Duplicate of A139426.

Original entry on oeis.org

1, 5, 1, 5, 11, 11, 17, 19, 23, 97, 127, 145, 167, 269, 767, 479, 3307, 1453, 18007, 2357, 599, 17669, 5527, 3191, 3251, 70249, 147773, 39637

Offset: 1

Pierre CAMI, Aug 11 2008

dead

All primes certified using PFGW from Primeform group.

			(2^2-1)*(2^2-1+1)-1=11 prime 2^2-1=M(1) so a(1)=1
(2^3-1)*(2^3-1+1)-1=55 composite
(2^3-1)*(2^3-1+3)-1=69 composite
(2^3-1)*(2^3-1+5)-1=83 prime 2^3-1=M(2) so a(2)=5

Cf. A000043 (Mersenne prime exponents), A143385.

Missing terms 2357 and 599 inserted by Jens Kruse Andersen, Jul 30 2014

A143387 Least prime a(n) such that M(n)(M(n)+a(n))-1 and M(n)(M(n)+a(n))+1 are twin primes with M(i)=i-th Mersenne prime A000043(i).

Original entry on oeis.org

3, 53, 11, 17, 317, 89, 1259, 2543, 7517, 16217, 15107, 33119, 60611, 671063, 2648057

Offset: 1

Pierre CAMI, Aug 11 2008

Cf. A000043, A139426, A143385, A143386.

cp's OEIS Frontend

A139426 Smallest number k such that M(n)^2+k*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A143384 Duplicate of A139426.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A143387 Least prime a(n) such that M(n)(M(n)+a(n))-1 and M(n)(M(n)+a(n))+1 are twin primes with M(i)=i-th Mersenne prime A000043(i).

Views

Author

Keywords

Crossrefs

cp's OEIS Frontend

A139426 Smallest number k such that M(n)^2+k*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A143384 Duplicate of A139426.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A143387 Least prime a(n) such that M(n)*(M(n)+a(n))-1 and M(n)*(M(n)+a(n))+1 are twin primes with M(i)=i-th Mersenne prime A000043(i).

Views

Author

Keywords

Crossrefs

A143387 Least prime a(n) such that M(n)(M(n)+a(n))-1 and M(n)(M(n)+a(n))+1 are twin primes with M(i)=i-th Mersenne prime A000043(i).