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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
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
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
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