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.

A087680 Numbers n such that n + 4 and n - 4 are both prime.

Original entry on oeis.org

7, 9, 15, 27, 33, 57, 63, 75, 93, 105, 135, 153, 177, 195, 237, 267, 273, 363, 393, 405, 435, 453, 483, 495, 567, 573, 597, 603, 657, 687, 705, 723, 747, 765, 825, 915, 933, 987, 1017, 1035, 1065, 1113, 1167, 1197, 1227, 1233, 1287, 1293, 1323, 1377, 1443
Offset: 1

Views

Author

Zak Seidov, Sep 27 2003

Keywords

Comments

All terms > 7 (prime) are divisible by 3. Also note that n-4 and n+4 are not necessarily consecutive primes. First case when n-4 and n+4 are consecutive primes is for n=93 with n-4=89 and n+4=97. - Zak Seidov, Apr 22 2015

Links

Crossrefs

Cf. A023202, A014574, A087678-A087683, A087695-A087697, A088764.

Programs

  • Maple
    ZL:=[]:for p from 1 to 1444 do if (isprime(p) and isprime(p+8) ) then ZL:=[op(ZL),(p+(p+8))/2]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007
  • Mathematica
    f[n_]:=PrimeQ[n-4]&&PrimeQ[n+4]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,3,8!,2}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 09 2009 *)
Select[Prime[Range[250]],PrimeQ[#+8]&]+4 (* Harvey P. Dale, May 21 2023 *)

Formula

a(n) = A023202(n) + 4. - Michel Marcus, Apr 22 2015

Extensions

More terms from Ray Chandler, Oct 26 2003

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.

A088766 a(n) = (A087681(n)-1)/2.

Original entry on oeis.org

5, 6, 8, 11, 12, 17, 18, 23, 26, 32, 33, 36, 38, 47, 51, 53, 66, 71, 72, 78, 86, 92, 93, 102, 108, 116, 117, 122, 128, 131, 137, 138, 143, 171, 176, 186, 197, 201, 207, 212, 213, 218, 227, 236, 242, 246, 248, 257, 281, 296, 303, 306, 312, 318, 323, 326, 333, 366
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Comments

Numbers k such that 2*k + 1 - 6 and 2*k + 1 + 6 are sexy primes. [Jonathan Vos Post, Feb 14 2011]

Examples

			1002 is in the sequence because 2*1002 + 1 - 6 = 1999 is prime, and 2*1002 + 1 + 6 = 2011 is prime.

Links

Crossrefs

Cf. A023201, A046117, A087681, A088762, A088764, A088765, A088768, A088770, A186243.

Programs

  • Magma
    [n-1: n in [3..400] |IsPrime(2*n+5) and IsPrime(2*n-7)]; // Vincenzo Librandi, May 20 2017
  • Mathematica
    Select[Range[3, 1000], PrimeQ[2 # + 5] && PrimeQ[2 # - 7] &] - 1 (* Vincenzo Librandi, May 20 2017 *)

Formula

{k such that 2*k + 1 - 6 is in A023201} = {k such that 2*k + 1 + 6 is in A046117}.

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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