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 1-6 of 6 results.

A087696 Numbers n such that n + 5 and n - 5 are both prime.

Original entry on oeis.org

8, 12, 18, 24, 36, 42, 48, 66, 78, 84, 102, 108, 132, 144, 162, 168, 186, 228, 234, 246, 276, 288, 312, 342, 354, 378, 384, 414, 426, 438, 444, 462, 504, 552, 582, 612, 636, 648, 678, 696, 714, 738, 756, 792, 816, 834, 858, 882, 924, 942, 972
Offset: 1

Views

Author

Zak Seidov, Sep 27 2003

Keywords

Links

Crossrefs

Cf. A014574, A087678-A087683, A087695-A087697, A088765.

Programs

  • Mathematica
    Select[Range[5,1000],AllTrue[#+{5,-5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 08 2014 *)
  • PARI
    isok(n) = isprime(n-5) && isprime(n+5); \\ Michel Marcus, Sep 02 2019

A186243 Numbers k such that 6*k-5 and 6*k-1 are both primes.

Original entry on oeis.org

2, 3, 4, 7, 8, 12, 14, 17, 18, 19, 22, 28, 33, 38, 39, 47, 52, 53, 59, 64, 67, 74, 77, 78, 82, 84, 103, 108, 113, 124, 127, 129, 138, 143, 144, 147, 148, 152, 157, 162, 169, 182, 183, 203, 214, 217, 218, 238, 239, 242, 248, 249, 259, 262, 264, 267, 269
Offset: 1

Views

Author

Jonathan Vos Post, Feb 15 2011

Keywords

Comments

Numbers k such that 6*k-5 and 6*k-1 are cousin primes. The D = 2 numbers in class II, from page 3 of Weber. - Jonathan Vos Post, Feb 14 2011

Examples

			a(3) = 4 because 6*4-5 = 19 is prime, and 6*4-1 = 23 is prime.

Links

Crossrefs

Cf. A023200, A046132, A088765.

Programs

  • Mathematica
    Select[Range[400], PrimeQ[6#-5] && PrimeQ[6#-1] &] (* Alonso del Arte, Feb 16 2011 *)

Formula

{k such that 6*k-5 is in A023200} = {k such that 6*k-1 is in A046132}.

A088763 a(n) = A087695(n)/2.

Original entry on oeis.org

4, 5, 7, 8, 10, 13, 17, 20, 22, 25, 28, 32, 35, 38, 43, 50, 52, 53, 55, 67, 77, 80, 85, 88, 97, 98, 113, 115, 118, 127, 130, 133, 137, 140, 155, 157, 167, 175, 178, 185, 188, 193, 218, 223, 230, 232, 253, 272, 280, 283, 287, 295, 298, 302, 305, 308, 322, 325, 328, 340
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Comments

A260689(a(n),1) = A264526(a(n)) = 3. - Reinhard Zumkeller, Nov 17 2015

Links

Crossrefs

Cf. A087695, A040040, A088765, A088767, A088769.
Cf. A260689, A264526.

Programs

  • Haskell
    a088763 = flip div 2 . a087695  -- Reinhard Zumkeller, Nov 17 2015
  • Maple
    ZL:=[]:for p from 1 to 700 do if (isprime(p) and isprime(p+6) ) then ZL:=[op(ZL),(p+(p+6))/4]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007
  • Mathematica
    f[n_]:=PrimeQ[n-3]&&PrimeQ[n+3]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,2,8!,2}];lst/2 (* Vladimir Joseph Stephan Orlovsky, Oct 09 2009 *)

Extensions

Offset corrected by Reinhard Zumkeller, Nov 17 2015

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}.

A088769 a(n) = A087678(n)/2.

Original entry on oeis.org

7, 10, 11, 14, 16, 19, 25, 26, 31, 35, 40, 44, 46, 49, 59, 61, 70, 74, 79, 86, 91, 94, 95, 101, 110, 116, 121, 124, 130, 136, 151, 161, 170, 179, 194, 196, 205, 215, 220, 224, 226, 229, 235, 250, 256, 266, 289, 304, 305, 311, 325, 326, 334, 341, 346, 350, 355
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Links

Crossrefs

Cf. A087678, A040040, A088763, A088765, A088767.

Programs

  • Magma
    [n/2: n in [5..1500] |IsPrime(n+9) and IsPrime(n-9)]; // Vincenzo Librandi, May 22 2017
  • Mathematica
    Select[Range[5, 2000], PrimeQ[# + 9] && PrimeQ[# - 9] &] / 2 (* Vincenzo Librandi, May 21 2017 *)

A088767 a(n) = A087697(n)/2.

Original entry on oeis.org

5, 6, 12, 15, 18, 27, 30, 33, 45, 48, 60, 72, 78, 87, 93, 102, 117, 132, 135, 138, 150, 162, 180, 183, 195, 213, 225, 228, 258, 282, 285, 297, 300, 303, 312, 327, 333, 342, 363, 375, 390, 402, 408, 423, 435, 480, 492, 495, 513, 528, 555, 558, 597, 612, 615, 642
Offset: 1

Views

Author

Ray Chandler, Oct 26 2003

Keywords

Comments

Numbers n such that 2*n-7 [A089192] and 2*n+7 [A105760] are both prime. [Vincenzo Librandi, Jul 10 2010]

Crossrefs

Cf. A087697, A040040, A088763, A088765, A088769.
Cf. A089192, A105760. [Vincenzo Librandi, Jan 18 2009]
Showing 1-6 of 6 results.

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