A121370 -id:A121370 - cp's OEIS frontend

A137908 Duplicate of A121370.

1, 3, 1, 7, 8, 19, 13, 4, 16, 3, 42, 24, 434, 84, 160, 579, 475, 529, 2450, 2644, 3928, 558, 13680, 7146, 1408, 3003, 2369, 55000, 83873

Offset: 1

dead

A121371 Least number k such that (kM(n))^2 + kM(n) - 1 and (kM(n))^2 + kM(n) + 1 are twin primes where M(n) is the n-th Mersenne prime.

Original entry on oeis.org

1, 3, 5, 8, 99, 275, 278, 404, 96, 1538, 1253, 15858, 189168, 119552, 221444, 1047122, 3571449, 5424924, 1575995

Offset: 1

Pierre CAMI, Jul 24 2006

			M(2) = 2^3-1 = 7, 7^2+7-1 = 55 is composite, (2*7)^2+2*7-1 = 209 is composite,
(3*7)^2+3*7-1 = 461 is prime, 461 and 463 are twin primes, so a(2) = 3.

Cf. A000043, A000668, A001097, A121370.

f[p_] := Module[{k = 1}, While[!PrimeQ[(k*p)^2 + k*p - 1] || !PrimeQ[(k*p)^2 + k*p + 1], k++]; k]; f /@ (2^MersennePrimeExponent[Range[10]] - 1) (* Amiram Eldar, Jul 23 2021 *)

a(8) corrected and a(18)-a(19) added by Amiram Eldar, Jul 23 2021

A200655 a(n)= least number k > a(n-1) such that k(2^p-1)(k*(2^p-1)+1)-1 is prime, where p = A000043(n) = Mersenne exponents.

Original entry on oeis.org

1, 3, 5, 7, 8, 19, 20, 23, 96, 190, 312, 400, 434, 852, 980, 1063, 1208, 3960, 5464, 6694, 7178, 13118, 13680, 18803, 27445, 28541, 42031, 73209, 83873

Offset: 1

Pierre CAMI, Nov 21 2011

nonn

a(n) is not so far from p

All certified primes using PFGW64 from primeform group

Cf. A000043, A121370

cp's OEIS Frontend

A137908 Duplicate of A121370.

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A121371 Least number k such that (kM(n))^2 + kM(n) - 1 and (kM(n))^2 + kM(n) + 1 are twin primes where M(n) is the n-th Mersenne prime.

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A200655 a(n)= least number k > a(n-1) such that k(2^p-1)(k*(2^p-1)+1)-1 is prime, where p = A000043(n) = Mersenne exponents.

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cp's OEIS Frontend

A137908 Duplicate of A121370.

Views

Author

Keywords

A121371 Least number k such that (k*M(n))^2 + k*M(n) - 1 and (k*M(n))^2 + k*M(n) + 1 are twin primes where M(n) is the n-th Mersenne prime.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A200655 a(n)= least number k > a(n-1) such that k*(2^p-1)*(k*(2^p-1)+1)-1 is prime, where p = A000043(n) = Mersenne exponents.

Views

Author

Keywords

Comments

Crossrefs

A121371 Least number k such that (kM(n))^2 + kM(n) - 1 and (kM(n))^2 + kM(n) + 1 are twin primes where M(n) is the n-th Mersenne prime.

A200655 a(n)= least number k > a(n-1) such that k(2^p-1)(k*(2^p-1)+1)-1 is prime, where p = A000043(n) = Mersenne exponents.