A100276 a(0)=3; for n > 0, a(n) = smallest prime > a(n-1) such that Product_{i=0..n} a(i) - 2 is prime.

3, 5, 7, 11, 13, 17, 19, 23, 59, 71, 73, 83, 89, 97, 191, 337, 359, 433, 569, 617, 643, 691, 809, 811, 1439, 1447, 1451, 1553, 1571, 1741, 1993, 2141, 2339, 2477, 2693, 2791, 2887, 2917, 4021, 5039, 5431, 5581, 5857, 6353, 6521, 6529, 6857, 7211, 7591, 7883

Offset: 0

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net), Dec 29 2004

Keywords

• nonn

Examples

			3*5-2=13 is prime;
3*5*7-2=103 is prime;
3*5*7*11-2=1153 is prime;
3*5*7*11*13-2=15013 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..100

Crossrefs

See A100277 for the resulting primes. Cf. A085013, A100301.

Programs

Mathematica

nxt[{pr_,a_}]:=Module[{p=NextPrime[a]},While[CompositeQ[pr*p-2],p=NextPrime[p]];{pr*p,p}]; NestList[nxt,{3,3},50][[;;,2]] (* Harvey P. Dale, Mar 30 2024 *)

Extensions

Corrected and extended by Emeric Deutsch, Mar 26 2005

More terms from Ryan Propper, Jan 11 2008