A097491 Primes which are two greater than the terms of A079164.

5, 17, 21800053277, 72409291238312731227527, 86984485062381462583582279727, 21679097826151232817152558557032490897727272048343000297777, 107025222275017133994159705286756083545279583250537082122450588876727

Offset

1,1

Comments

A097491(8) = 2948...794027 has 76 digits and A097491(9) = 152400...802327 has 288 digits. - Hartmut F. W. Hoft, Apr 27 2021

Links

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

Example

a(3) = 21800053277 = A079164(17) + 2 = 3*5*5*7*11*13*17*19*29*31 + 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}]
pairList[n_] := First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]
a079164[n_] := Rest[FoldList[Times, 1, Take[Flatten[pairList[n]], n]]]
a097491[n_] := Select[Map[#+2&, a079164[n]], PrimeQ]
a097491[39] (* Hartmut F. W. Hoft, Apr 27 2021 *)

Prog

(PARI) ft(n) = p=1; for(x=1, n, p*=twinl(x); if(isprime(p+2), print1(p+2", ")); p*=twinu(x); if(isprime(p+2), print1(p+2", "))) \The n-th lower twin prime 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 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. A048599, A097490, A097493.

Cf. A037074, A077800, A079164.

Sequence in context: A363759 A116911 A351890 * A120087 A353690 A180135

Adjacent sequences: A097488 A097489 A097490 * A097492 A097493 A097494

Keyword

nonn

Author

Cino Hilliard, Aug 24 2004

Extensions

Edited by Don Reble, Apr 16 2007

Correction in name. - Hartmut F. W. Hoft, Apr 27 2021

Status

approved