A128662 Numbers k such that p(k+1)# + p(k)# - p(k-1)# + 1 is prime where p(i)# = product of first i primes = A002110(i).

8, 13, 14, 15, 30, 41, 71, 85, 97, 132, 221, 282, 424, 509, 1346, 1348, 3684, 8224

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Mathematica

Flatten[Position[Partition[FoldList[Times, Prime[Range[1350]]], 3, 1], _?(PrimeQ[ #[[2]]+#[[3]]-#[[1]]+1]&), 1, Heads->False]]+1 (* Harvey P. Dale, May 30 2018 *)

Prog

(PARI) P(n) = factorback(primes(n)); \\ A002110
isok(k) = ispseudoprime(P(k+1)+P(k)-P(k-1)+1); \\ Michel Marcus, Sep 11 2022

Crossrefs

Cf. A002110, A128420, A128421, A128657, A128658, A128659, A128660, A128661.

Sequence in context: A382711 A335167 A124159 * A133192 A063684 A059194

Adjacent sequences: A128659 A128660 A128661 * A128663 A128664 A128665

Keyword

nonn,more

Author

Pierre CAMI, Mar 19 2007

Extensions

a(17) from Michael S. Branicky, Jun 23 2023

a(11) corrected and a(18) from Michael S. Branicky, Dec 11 2024

Status

approved