cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

5, 17, 21800053277, 72409291238312731227527, 86984485062381462583582279727, 21679097826151232817152558557032490897727272048343000297777, 107025222275017133994159705286756083545279583250537082122450588876727
Offset: 1

Views

Author

Cino Hilliard, Aug 24 2004

Keywords

Comments

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

Examples

			a(3) = 21800053277 = A079164(17) + 2 = 3*5*5*7*11*13*17*19*29*31 + 2. - _Hartmut F. W. Hoft_, Apr 27 2021

Links

Crossrefs

Cf. A048599, A097490, A097493.
Cf. A037074, A077800, A079164.

Programs

  • 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 *)
  • 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

Extensions

Edited by Don Reble, Apr 16 2007
Name corrected by Hartmut F. W. Hoft, Apr 27 2021

A074040 Product of first n twin prime pair products.

Original entry on oeis.org

15, 525, 75075, 24249225, 21800053275, 38433493923825, 138322144631846175, 716923675626858725025, 7458156997546211316435075, 86984485062381462583582279725, 1656445549042930191979157352803175
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 13 2002

Keywords

Examples

			The first two twin prime pairs are (3,5) and (5,7), their products: 15 and 35, therefore a(2)=15*35=525.

Crossrefs

Cf. A074041, A001359, A006512 & A014574.
Cf. A037074, A077800, A079164.

Programs

  • Mathematica
    a = {4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150} (* A014574 *); Table[ Product[a[[k]]^2 - 1, {k, 1, n}], {n, 1, 12}]
Rest[FoldList[Times,1,Times@@@Select[Partition[Prime[Range[50]],2,1],#[[2]]-#[[1]]==2&]]] (* Harvey P. Dale, Jan 19 2015 *)
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&]]
a037074[n_] := Map[Apply[Times, #]&, pairList[n]]
a074040[n_] := Rest[FoldList[Times, 1, a037074[n]]]
a074040[11] (* Hartmut F. W. Hoft, Apr 27 2021 *)

Formula

a(1) = A037074(1) and a(n) = a(n-1)*A037074(n) for n>1.
a(n) = A079164(2*n).

Extensions

Edited by Robert G. Wilson v, Aug 17 2002
Corrections in Comment and Example, and added references. Hartmut F. W. Hoft, Apr 27 2021

A344147 Primes in A191746.

Original entry on oeis.org

193, 53069, 58422233, 1348470667, 2847740783, 3237916229, 5029745827, 7643871979, 15107731019, 17902513283, 21052092827, 22187962591, 28412311451, 59363922119, 81459096899, 85780812149, 102742076659, 123894775231, 137692362377, 143889901511, 170038274723, 174648621811
Offset: 1

Views

Author

Hartmut F. W. Hoft, May 10 2021

Keywords

Examples

			a(1)=193=A191746(3) is the first prime in A191746 and a(2)=53069=A191746(11) is the second.

Crossrefs

Cf. A037074, A074040, A077800, A079164, A191746.

Programs

  • Mathematica
    (* function a037074[ ] and support functions are defined in A074040 *)
a191746[n_] := Rest[FoldList[Plus, 0, a037074[n]]]
a344147x[n_] := Select[a191746[n], PrimeQ]
a344147[550]

A344148 Primes which are two greater than A191746 terms.

Original entry on oeis.org

17, 6779, 293617, 2992417, 24101863, 423722581, 625997497, 929306267, 3377032037, 3825265007, 6458885659, 7150892197, 13075407803, 13860035251, 19434399319, 32531231209, 47475445333, 50281049527, 53207636077, 62607479491, 85780812151, 106014038789, 109384656937, 121991823731, 125813698531
Offset: 1

Views

Author

Hartmut F. W. Hoft, May 10 2021

Keywords

Comments

Among numbers a(1..564) are 38 twin primes of which 14 are twins to numbers in A344147 with the first of the latter pairs being A344147(16)=85780812149 and a(21)=85780812151. In contrast it appears that A097490, A097491, A097493 and A343778 contain only twin prime numbers from the set {5, 7, 17}.

Examples

			a(1)=17=A191746(1)+2 is the first prime and a(2)=6779=A191746(7)+2 is the second of the form A191746(k)+2; both are twin primes while a(3)=293617 is not.

Crossrefs

Cf. A037074, A074040, A077800, A079164, A097490, A097491, A097493, A191746, A344147.

Programs

  • Mathematica
    (* function a191746[ ] is defined in A344147 *)
a344148[n_] := Select[a191746[n] + 2, PrimeQ]
a344148[500]
Showing 1-4 of 4 results.

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