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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A000043, A000668, A001097, A121370.

Sequence in context: A174529 A174442 A109342 * A067094 A272235 A058642

Adjacent sequences: A121368 A121369 A121370 * A121372 A121373 A121374

Keyword

nonn,hard,more

Author

Pierre CAMI, Jul 24 2006

Extensions

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

Status

approved