A112229 Table of the smallest (x,y) pairs such that x*n+1 is prime, y*n+1 is a larger prime, and (x*n+1)*(y*n+1)-2 is also prime.

2, 4, 1, 2, 2, 4, 1, 4, 2, 8, 1, 2, 4, 28, 2, 11, 2, 4, 1, 4, 2, 32, 1, 3, 4, 40, 2, 14, 2, 4, 1, 37, 6, 138, 1, 2, 10, 40, 2, 5, 2, 16, 1, 16, 2, 26, 3, 4, 4, 10, 2, 20, 4, 10, 1, 7, 2, 50, 1, 2, 10, 22, 3, 6, 2, 6, 3, 69, 2, 8, 1, 2, 4, 40, 5, 20, 2, 4, 1, 7, 2, 20, 1, 8, 4, 10, 2, 32, 4, 12, 1, 13

Offset

1,1

Comments

The associated (x*n+1)*(y*n+1) for a solution is a semiprime, so the (x*n+1)*(y*n+1)-2 are actually Chen primes.

If more than one pair exists for a given n, priority is given to minimize x, the smaller prime.

Links

Table of n, a(n) for n=1..92.

Example

For n=3, (x,y)=(2,4), 2*3+1=7 is prime, 4*3+1=13 is prime, and 7*13-2=89 is a Chen prime.
2,4;
1,2;
2,4;
1,4;
2,8;
1,2;
4,28;
2,11;
2,4;
1,4;
2,32;
1,3;
4,40;...

Crossrefs

Cf. A112230.

Sequence in context: A208645 A361381 A054708 * A087419 A338095 A050979

Adjacent sequences: A112226 A112227 A112228 * A112230 A112231 A112232

Keyword

nonn,tabf

Author

Pierre CAMI, Aug 29 2005

Status

approved