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 1-5 of 5 results.

A343778 Primes which are two greater than A074040 terms.

Original entry on oeis.org

17, 21800053277, 86984485062381462583582279727, 2948338207972508983453357158259221375675126583677039825367935271466652794027
Offset: 1

Views

Author

Hartmut F. W. Hoft, Apr 29 2021

Keywords

Comments

a(5) = 3052230...330677 has 17332 digits, the only prime larger than a(4) and among the cumulative products of the first 2000 twin primes pairs plus two.

Examples

			a(1) = 17 = A074040(1) + 2 = 3*5 + 2.

Crossrefs

Cf. A037074, A077800, A074040, A097490, A097491, A097493.

Programs

  • Mathematica
    (* function a074040[ ] is defined in A074040 *)
a343778[n_] := Select[Map[#+2&, a074040[n]], PrimeQ]
a343778[30]

A057130 Product of first n primes of form 6k-1.

Original entry on oeis.org

5, 55, 935, 21505, 623645, 25569445, 1201763915, 63693487495, 3757915762205, 266812019116555, 22145397586674065, 1970940385213991785, 199064978906613170285, 21299952743007609220495, 2406894659959859841915935, 315303200454741639290987485
Offset: 1

Views

Author

Henry Bottomley, Aug 11 2000

Keywords

Examples

			a(3) = 5*11*17 = 935.
a(4) = 21505 = 5 * 11 * 17 * 23.

Crossrefs

Cf. A000040, A002110, A002476, A006278, A007528, A074040, A078586, A121940.
Cf. A008543, A057131.

Programs

  • PARI
    lista(nn) = {pp = 1; for (n = 1, nn, p = prime(n); if (Mod(p, 6) == -1, pp *= p; print1(pp, ", ")););} \\ Michel Marcus, Sep 08 2013

Formula

a(n) = a(n-1)*A007528(n) = (A057131(n)+1)/6.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 06 2000
More terms from Michel Marcus, Sep 08 2013

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]

A074041 Product of first n single (i.e., non-twin) primes.

Original entry on oeis.org

2, 46, 1702, 79994, 4239682, 284058694, 22440636826, 1862572856558, 165768984233662, 16079591470665214, 1816993836185169182, 230758217195516486114, 30229326452612659680934, 4746004253060187569906638, 773598693248810573894781994
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 13 2002

Keywords

Comments

a(n) = 5*A002110(A049084(A074038(n)))/A074040(k), where k is the largest number such that A006512(k) < A007510(n).

Examples

			The first four single primes are 2, 23, 37 and 47, therefore a(4) = 2*23*37*47 = 79994.

Programs

  • Mathematica
    nn=50;tps=Union[Flatten[Select[Partition[Prime[Range[nn]],2,1],Last[#]- First[#] ==2&]]]; ntps=Complement[Prime[Range[nn]],tps];Rest[ FoldList[ Times,1,ntps]]  (* Harvey P. Dale, Mar 31 2011 *)

Formula

a(1) = A007510(1) and a(n) = a(n-1)*A007510(n) for n > 1.

Extensions

More terms from Harvey P. Dale, Mar 31 2011

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 1-5 of 5 results.

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