A053982 Numbers k such that 1 + product of first k composite numbers is prime.
1, 3, 7, 11, 16, 22, 39, 76, 116, 139, 149, 169, 179, 220, 372, 429, 1216, 2146, 3176, 5382, 5969, 12271, 15271, 43903
Offset: 1
Programs
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Mathematica
Composite[n_Integer] := (k = n + PrimePi[n] + 1; While[k - PrimePi[k] - 1 != n, k++ ]; k); Do[ If[ PrimeQ[ Product[ Composite[k], {k, 1, n} ] + 1], Print[ n ] ], {n, 1, 430} ] Position[FoldList[Times,Select[Range[1500],CompositeQ]],?(PrimeQ[#+1]&)]//Flatten (* _Harvey P. Dale, Dec 20 2022 *) -
PARI
lista(kmax) = {my(m = 1, k = 0); forcomposite(c = 1, , k++; if(k > kmax, break); m *= c; if(isprime(m+1), print1(k, ", ")));} \\ Amiram Eldar, Jun 03 2024
Extensions
More terms from Jeppe Stig Nielsen, Apr 16 2000 (terms from 76 on correspond to probable primes)
a(16)-a(17) from Robert G. Wilson v, Apr 20 2001
Edited by T. D. Noe, Oct 30 2008
a(18)-a(19) from Amiram Eldar, Jun 03 2024
a(20)-a(21) from Michael S. Branicky, Jun 04 2024
More terms via A049420 from Jeppe Stig Nielsen, Aug 12 2024