Voozh

A097493

Primes which are two greater than A097492 terms.

7, 37, 457, 8647, 51315414607

OFFSET

1,1

COMMENTS

The next term (17866..79237) has 186 digits.

LINKS

EXAMPLE

a(4) = 8647 = (Product_{k=1..4} A006512(k)) + 2 = 5*7*13*19 + 2 = A097492(4) + 2. - Hartmut F. W. Hoft, Apr 27 2021

MATHEMATICA

step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p, p+2}}, {}]], p}]

largerTwin[n_] := Last[Transpose[First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]]]

a097492[n_] := Rest[FoldList[Times, 1, largerTwin[n]]]

a097493[n_] := Select[Map[#+2&, a097492[n]], PrimeQ]

a097493[68] (* Hartmut F. W. Hoft, Apr 27 2021 *)

PROG

(PARI) fu(n) = p=1; for(x=1, n, p*=twinu(x); if(isprime(p+2), print1(p+2", ")))

twinu(n) = { local(c, x); c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++; ); return(prime(x)) }

CROSSREFS

KEYWORD

nonn

AUTHOR

EXTENSIONS

Edited by Don Reble, Apr 16 2007

STATUS

approved

URL: https://oeis.org/A097493