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

Table of n, a(n) for n=1..5.

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", "))) \The n-th upper twin prime 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