A093192 If M(n) is the n-th Mersenne prime, then a(n) is the smallest positive integer such that 2*a(n)*M(n)*M(n+1)*M(n+2)-1 is prime.

1, 1, 21, 1, 12, 16, 6, 112, 76, 195, 61, 21, 511, 909, 1689, 517, 640, 487, 13615, 12547, 382, 60456

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Example

a(3) = 21: M(3) = 2^5-1 = 31; M(4) = 2^7-1 = 127; M(5) = 2^13-1 = 8191; 2*21*31*127*8191-1 = 1354414613, which is prime.

Mathematica

spi[n_]:=Module[{k=2}, While[!PrimeQ[k*n-1], k+=2]; k/2]; spi/@Times@@@ Partition[ Select[2^Range[5000]-1, PrimeQ], 3, 1] (* The program generates the first 18 terms of the sequence. To generate more terms, increase the Range specification constant, but the program may take a long time to run. *) (* Harvey P. Dale, Dec 09 2018 *)

Crossrefs

Sequence in context: A040456 A040457 A040458 * A040459 A040460 A040461

Adjacent sequences: A093189 A093190 A093191 * A093193 A093194 A093195

Keyword

nonn

Author

Ray G. Opao, Apr 21 2004

Status

approved