A387039 Numbers k such that (p_k#)*(p_(k-1)#)+1, or A228593(k)+1 is prime.

1, 2, 3, 4, 5, 6, 11, 12, 35, 617

Offset: 1

Author

Arsen Vardanyan, Aug 14 2025

Keywords

• nonn
• more

Examples

			4 is a term since (p_4#)(p_3#) + 1 = (7*5*3*2)(5*3*2) + 1 = 210*30 + 1 = 6301 is prime.
		

Crossrefs

Cf. A000040, A002110, A034386, A228593, A006094.

Programs

Maple

p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
q:= k-> isprime(p(k)*p(k-1)+1):
select(q, [$1..50])[];  # Alois P. Heinz, Aug 14 2025

Mathematica

Position[Times @@@ Partition[FoldList[Times, 1, Prime@ Range[400]], 2, 1] + 1, ?PrimeQ][[All, 1]] (* _Michael De Vlieger, Aug 23 2025 *)

PARI

isok(k) = isprime(vecprod(primes(k))*vecprod(primes(k-1))+1);

Extensions

a(10) from Michael S. Branicky, Aug 14 2025