

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.


1



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
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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*132=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: A133902 A208645 A054708 * A087419 A050979 A053450
Adjacent sequences: A112226 A112227 A112228 * A112230 A112231 A112232


KEYWORD

nonn,tabf


AUTHOR

Pierre CAMI, Aug 29 2005


STATUS

approved



