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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 (list; graph; refs; listen; history; text; internal format)
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: A265823 A208645 A054708 * A087419 A050979 A053450

Adjacent sequences:  A112226 A112227 A112228 * A112230 A112231 A112232

KEYWORD

nonn,tabf

AUTHOR

Pierre CAMI, Aug 29 2005

STATUS

approved

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Last modified December 8 12:55 EST 2016. Contains 278945 sequences.