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

Amiram Eldar, Table of n, a(n) for n = 1..7

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

Cf. A097490, A097491, A097492.

Cf. A001359, A077800, A097489.

Sequence in context: A330388 A371710 A276231 * A341377 A082687 A117731

Adjacent sequences: A097490 A097491 A097492 * A097494 A097495 A097496

Keyword

nonn

Author

Cino Hilliard, Aug 24 2004

Extensions

Edited by Don Reble, Apr 16 2007

Status

approved