A249798 Numbers k such that the product of the first k primes minus the (k+1)-th prime is prime.

3, 4, 5, 6, 8, 22, 23, 24, 35, 73, 83, 147, 553, 1098, 1115, 1542, 2097, 2149, 8712, 19965, 25046, 30987, 38635

Offset

1,1

Links

Table of n, a(n) for n=1..23.

Formula

a(n) = primepi(A093078(n)). - Michel Marcus, Nov 06 2014

Example

p(1)*p(2)*p(3)*p(4) - p(5) = 2*3*5*7 - 11 = 199. 199 is prime, therefore 4 is in the sequence.

Mathematica

Select[Range[1000], PrimeQ[Times@@(Prime[Range[#]])-Prime[#+1]]&]

Prog

(PARI) lista(nn) = {prp = 1; for(n=1, nn, prp *= prime(n); if (isprime(prp-prime(n+1)), print1(n, ", ")); ); } \\ Michel Marcus, Nov 06 2014

Crossrefs

Cf. A000040, A093078.

Sequence in context: A094576 A103103 A217347 * A037348 A277898 A212640

Adjacent sequences: A249795 A249796 A249797 * A249799 A249800 A249801

Keyword

nonn,more

Author

Ivan N. Ianakiev, Nov 06 2014

Extensions

a(17)-a(18) using A093078 from Michael S. Branicky, Mar 18 2024

a(19)-a(23) from Henri Lifchitz, Nov 08 2024

Status

approved