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

Amiram Eldar, Table of n, a(n) for n = 1..9

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

Name corrected by Hartmut F. W. Hoft, Apr 27 2021

Status

approved