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

1,2

Links

Table of n, a(n) for n=1..24.

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 *)

Prog

(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

Crossrefs

Cf. A002808, A000040, A049420, A049650, A057017, A140294.

Sequence in context: A118027 A082644 A131024 * A118000 A121640 A319258

Adjacent sequences: A053979 A053980 A053981 * A053983 A053984 A053985

Keyword

nonn,more

Author

G. L. Honaker, Jr., Apr 02 2000

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

Status

approved