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

1, 2, 3, 469

Offset

1,2

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

Links

Table of n, a(n) for n=1..4.

Example

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

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 *)

Prog

(PARI)
twinl(n) = { local(c, x); c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++; ); return(prime(x-1)) } \\ The n-th lower twin prime.
twiprimesl2(n, a) = { local(pr, x, y, j); for(a=0, n, for(j=1, n, pr=1; for(x=1, j, pr*=twinl(x); ); y=pr+2^a; if(ispseudoprime(y), print1(y", "); break ) ) ) } \\ Cino 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

Crossrefs

Cf. A097489.

Sequence in context: A109855 A306370 A355644 * A196070 A173342 A090510

Adjacent sequences: A128871 A128872 A128873 * A128875 A128876 A128877

Keyword

nonn,more

Author

Cino Hilliard, May 08 2007

Extensions

Partially edited by Michel Marcus, Feb 10 2014

Status

approved