A128874 Numbers k such that 16 + the product of the first k lesser twin primes (A097489) is prime.

1, 2, 3, 469

Offset: 1

Author

Cino Hilliard, May 08 2007

Keywords

• nonn
• more

Comments

Define twinl#(n)as the product of the first n lesser twin primes. Then if twinl#(n)+ 16 is prime, list n.

It is interesting from the example that the first three primes 19,31 and 181 greater than twinl#(n) + 16 are all greater twin primes. The next PRP is the 1824 digit number twinl#(469) + 16 and is not part of a twin prime pair.

a(5) > 2000, if it exists. - Amiram Eldar, Jul 07 2024

a(5) > 10000, if it exists. - Michael S. Branicky, Jul 11 2024

Examples

			Twinl#(3) + 16 = 3*5*11+16 = 181 is prime so 3 is in the sequence.
		

Crossrefs

Cf. A097489.

Programs

Mathematica

next[n_] := Module[{k = n + 1}, While[! (PrimeQ[k] && PrimeQ[k + 2]), k++]; k]; seq[kmax_] := Module[{r = 1, p = 1, s = {}}, Do[p = next[p]; r *= p; If[PrimeQ[r + 16], AppendTo[s, k]], {k, 1, kmax}]; s]; seq[500] (* Amiram Eldar, Jul 07 2024 *)

PARI

twinl(n) = { local(c,x); c=0; x=1; while(cCino Hilliard, May 08 2007

PARI

lista(nn) = { for(n=1, nn, if (ispseudoprime(16+prod(i=1, n, twinl(i))), print1(n, ", ")));} \\ Michel Marcus, Feb 10 2014

Extensions

Partially edited by Michel Marcus, Feb 10 2014