A180944 Primes such that their product with the successive prime plus the next successive prime plus 1 is a prime.

3, 5, 13, 17, 19, 29, 41, 47, 61, 67, 73, 97, 103, 107, 157, 191, 229, 277, 281, 283, 293, 307, 379, 401, 409, 491, 547, 557, 569, 607, 619, 659, 691, 701, 751, 773, 787, 823, 827, 853, 883, 887, 911, 971, 983, 997, 1031, 1039, 1049, 1109, 1129, 1153, 1171

Offset: 1

Author

Carmine Suriano, Sep 27 2010

Keywords

• nonn

Comments

prime(i)*prime(i+1) + prime(i+2) + 1 is prime.

In the sequence there are some twins: e.g. (281, 283) and (1949, 1951).

There are also successive primes such as (13,17,19); (277,281,283,293,307); (883,887).

Examples

			a(5)=19 since 19*23+29+1=467 is a prime.
		

Crossrefs

Cf. A000040.

Programs

Mathematica

#[[1]]&/@Select[Partition[Prime[Range[200]],3,1],PrimeQ[ #[[1]] #[[2]]+#[[3]]+1]&] (* Harvey P. Dale, Nov 07 2010 *)

Extensions

Missing values starting at 1031 inserted by R. J. Mathar, Oct 18 2010