A098817 a(n) is the least k such that k*Mersenne_prime(n)^2 - 1 and k*Mersenne_prime(n)^2 + 1 are twin primes.

2, 18, 72, 780, 228, 852, 228, 1080, 4020, 25800, 6012, 40332, 713502, 332880, 455892, 6428118, 4142652, 173808

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Example

2*((2^2-1)^2) - 1 = 17, 2*((2^2-1)^2) + 1 = 19; 17 and 19 are twin primes so a(1) = 2.

Mathematica

f[p_] := Module[{k = 1}, While[!PrimeQ[k*p^2 - 1] || !PrimeQ[k*p^2 + 1], k++]; k]; f /@ (2^MersennePrimeExponent[Range[10]] - 1) (* Amiram Eldar, Aug 28 2021 *)

Crossrefs

Cf. A000043, A000668, A001097.

Sequence in context: A120361 A120358 A152887 * A197093 A034473 A024171

Adjacent sequences: A098814 A098815 A098816 * A098818 A098819 A098820

Keyword

nonn,more

Author

Pierre CAMI, Oct 08 2004

Extensions

a(7) corrected, a(12) inserted and a(15)-a(18) added by Amiram Eldar, Aug 28 2021

Status

approved