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.

A087681 Numbers n such that n + 6 and n - 6 are both prime.

Original entry on oeis.org

11, 13, 17, 23, 25, 35, 37, 47, 53, 65, 67, 73, 77, 95, 103, 107, 133, 143, 145, 157, 173, 185, 187, 205, 217, 233, 235, 245, 257, 263, 275, 277, 287, 343, 353, 373, 395, 403, 415, 425, 427, 437, 455, 473, 485, 493, 497, 515, 563, 593, 607, 613, 625, 637, 647
Offset: 1

Views

Author

Zak Seidov, Sep 27 2003

Keywords

Comments

Many terms are of the form 5 + n + n^2 or 5 + 2*n^2: A054794.

Links

Crossrefs

Cf. A054794.
Cf. A014574, A087678-A087683, A087695-A087697, A088766.

Programs

  • Mathematica
    f[n_]:=PrimeQ[n-6]&&PrimeQ[n+6]; lst={}; Do[If[f[n],AppendTo[lst,n]],{n,2,7!,1}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 12 2009 *)
Select[Range[2,700],AllTrue[#+{6,-6},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 26 2019 *)

A088762 Numbers n such that (2n-1, 2n+3) is a cousin prime pair.

Original entry on oeis.org

2, 4, 7, 10, 19, 22, 34, 40, 49, 52, 55, 64, 82, 97, 112, 115, 139, 154, 157, 175, 190, 199, 220, 229, 232, 244, 250, 307, 322, 337, 370, 379, 385, 412, 427, 430, 439, 442, 454, 469, 484, 505, 544, 547, 607, 640, 649, 652, 712, 715, 724, 742, 745, 775, 784, 790
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Links

Crossrefs

Essentially the same as A111981.
Cf. A087679, A088764, A088766, A088768, A088770.

Programs

Formula

a(n) = (A087679(n)-1)/2 = (A023200(n)+1)/2 = (A046132(n)-3)/2.

A088764 a(n) = (A087680(n)-1)/2.

Original entry on oeis.org

3, 4, 7, 13, 16, 28, 31, 37, 46, 52, 67, 76, 88, 97, 118, 133, 136, 181, 196, 202, 217, 226, 241, 247, 283, 286, 298, 301, 328, 343, 352, 361, 373, 382, 412, 457, 466, 493, 508, 517, 532, 556, 583, 598, 613, 616, 643, 646, 661, 688, 721, 727, 742, 763, 781, 787
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Links

Crossrefs

Cf. A087680, A088762, A088766, A088768, A088770.

Programs

  • Magma
    [(n-1)/2: n in [2..2000] |IsPrime(n+4) and IsPrime(n-4)]; // Vincenzo Librandi, May 19 2017
  • Mathematica
    f[n_]:=PrimeQ[n - 4] && PrimeQ[n + 4]; lst={}; Do[If[f[n], AppendTo[lst, (n - 1) / 2]], {n, 3, 7!, 2}]; lst (* Vincenzo Librandi, May 19 2017 *)
(#-1)/2&/@(Select[Prime[Range[250]],PrimeQ[#+8]&]+4) (* Harvey P. Dale, May 21 2023 *)

A088768 a(n) = (A087682(n)-1)/2.

Original entry on oeis.org

5, 7, 10, 19, 22, 25, 37, 40, 52, 79, 82, 85, 94, 109, 115, 124, 142, 169, 172, 187, 190, 220, 235, 247, 274, 277, 289, 292, 304, 319, 325, 334, 367, 382, 409, 415, 472, 487, 502, 520, 547, 550, 589, 604, 610, 649, 655, 715, 739, 745, 775, 787, 802, 814, 850
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Links

Crossrefs

Cf. A087682, A088762, A088764, A088766, A088770.

Programs

  • Magma
    [(n-1)/2: n in [6..2000] |IsPrime(n+8) and IsPrime(n-8)]; // Vincenzo Librandi, May 20 2017
  • Mathematica
    Select[Range[6, 2000], PrimeQ[2 # + 7] && PrimeQ[2 # - 9] &] - 1 (* Vincenzo Librandi, May 20 2017 *)

A088770 a(n) = (A087683(n)-1)/2.

Original entry on oeis.org

6, 10, 13, 16, 25, 28, 31, 34, 46, 49, 58, 70, 73, 91, 94, 100, 130, 133, 136, 151, 160, 163, 178, 181, 184, 199, 205, 214, 226, 238, 244, 256, 265, 283, 298, 301, 304, 325, 331, 364, 409, 424, 433, 436, 448, 478, 490, 493, 511, 514, 520, 529, 553, 556, 559
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Links

Crossrefs

Cf. A087683, A088762, A088764, A088766, A088768.

Programs

  • Magma
    [(n-1)/2: n in [8..2000] |IsPrime(n+10) and IsPrime(n-10)]; // Vincenzo Librandi, May 22 2017
  • Mathematica
    Rest[f[n_]:=PrimeQ[n - 10] && PrimeQ[n + 10]; lst={}; Do[If[f[n], AppendTo[lst, (n - 1) / 2]], {n, 5, 7!, 2}]; lst] (* Vincenzo Librandi, May 22 2017 *)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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