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A097493 Primes which are two greater than A097492 terms. 4
7, 37, 457, 8647, 51315414607 (list; graph; refs; listen; history; text; internal format)
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: A093168 A330388 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

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Last modified January 24 21:49 EST 2022. Contains 350565 sequences. (Running on oeis4.)