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

0,1

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A128925 A204142 A131261 * A225669 A065389 A123567

Adjacent sequences: A100273 A100274 A100275 * A100277 A100278 A100279

Keyword

nonn

Author

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

Extensions

Corrected and extended by Emeric Deutsch, Mar 26 2005

More terms from Ryan Propper, Jan 11 2008

Status

approved