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

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, 29, 19, 37, 5, 7, 29, 3, 79, 43, 41, 3, 11, 53, 5, 13, 3, 29, 11, 137, 179, 227, 11, 11, 97, 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

Offset

0,1

Links

Pierre CAMI, Table of n, a(n) for n = 0..2642

Mathematica

Table[p=3; prod=6; While[! PrimeQ[prod*2^n-1], p=NextPrime[p]; prod=prod*p]; p, {n, 0, 100}]

Prog

PFGW SCRIPTIFY PROGRAM
  Prime P in pfgw.log file
  command : pfgw -f in.txt
  in.txt file follows
SCRIPT
DIM nn, -1
DIM kk
DIMS tt
LABEL loopn
SET nn, nn+1
SET kk, 1
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; p(kk)
PRP p(kk)#*2^nn-1, tt
IF !(ISPRP || ISPRIME) THEN GOTO loopk
GOTO loopn
(Sage) primorial = lambda n: prod(primes(n+1)) # includes n, if prime
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

Crossrefs

Cf. A085427.

Sequence in context: A328914 A295084 A068048 * A264050 A262995 A125713

Adjacent sequences: A176991 A176992 A176993 * A176995 A176996 A176997

Keyword

nonn

Author

Pierre CAMI, Dec 08 2010

Status

approved