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A176994 Least odd prime p such that p#*2^n-1 is prime, with p# the primorial A034386(p).

%I A176994 #24 Mar 13 2014 00:56:01
%S A176994 3,3,3,3,5,3,3,7,7,5,3,109,17,5,13,17,5,3,17,67,11,89,13,17,7,89,31,
%T A176994 29,19,37,5,7,29,3,79,43,41,3,11,53,5,13,3,29,11,137,179,227,11,11,97,
%U A176994 59,53,11,3,83,17,47,19,19,29,73,41,3,7,11,79,71,13,41,257,19,5,151,79,3,31,19,79,5,281,5,37,263,139,17,23,127,223,151,149,131,113,3,47,41,59,31,23,89
%N A176994 Least odd prime p such that p#*2^n-1 is prime, with p# the primorial A034386(p).
%H A176994 Pierre CAMI, <a href="/A176994/b176994.txt">Table of n, a(n) for n = 0..2642</a>
%t A176994 Table[p=3; prod=6; While[! PrimeQ[prod*2^n-1], p=NextPrime[p]; prod=prod*p]; p, {n, 0, 100}]
%o A176994 PFGW SCRIPTIFY PROGRAM
%o A176994   Prime P in pfgw.log file
%o A176994   command : pfgw -f in.txt
%o A176994   in.txt file follows
%o A176994 SCRIPT
%o A176994 DIM nn,-1
%o A176994 DIM kk
%o A176994 DIMS tt
%o A176994 LABEL loopn
%o A176994 SET nn,nn+1
%o A176994 SET kk,1
%o A176994 LABEL loopk
%o A176994 SET kk,kk+1
%o A176994 SETS tt,%d,%d\,;nn;p(kk)
%o A176994 PRP p(kk)#*2^nn-1,tt
%o A176994 IF !(ISPRP || ISPRIME) THEN GOTO loopk
%o A176994 GOTO loopn
%o A176994 (Sage) primorial = lambda n: prod(primes(n+1)) # includes n, if prime
%o A176994 A176994 = lambda n: next(p for p in Primes() if p > 2 and is_pseudoprime(primorial(p)*2**n-1)) # _D. S. McNeil_, Dec 09 2010
%Y A176994 Cf. A085427.
%K A176994 nonn
%O A176994 0,1
%A A176994 _Pierre CAMI_, Dec 08 2010