A088767 -id:A088767 - cp's OEIS frontend

A087697 Numbers k such that k + 7 and k - 7 are both prime.

10, 12, 24, 30, 36, 54, 60, 66, 90, 96, 120, 144, 156, 174, 186, 204, 234, 264, 270, 276, 300, 324, 360, 366, 390, 426, 450, 456, 516, 564, 570, 594, 600, 606, 624, 654, 666, 684, 726, 750, 780, 804, 816, 846, 870, 960, 984, 990

Offset: 1

Zak Seidov, Sep 27 2003

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A014574, A087678, A087679, A087680, A087681, A087682, A087683, A087695, A087696, A088767.

[n: n in [5..1000] | IsPrime(n-7) and IsPrime(n+7)]; // Vincenzo Librandi, Jul 23 2018

select(t -> isprime(t+7) and isprime(t-7), [seq(i,i=8..1000,2)]); # Robert Israel, Jul 22 2018

Rest[Select[Range[1000], PrimeQ[# - 7] && PrimeQ[# + 7] &]] (* Vincenzo Librandi, Jul 23 2018 *)

isok(n) = isprime(n-7) && isprime(n+7); \\ Michel Marcus, Jul 23 2018

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

Ray Chandler, Oct 26 2003

nonn

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Cf. A260689, A264526.

a088763 = flip div 2 . a087695  -- Reinhard Zumkeller, Nov 17 2015

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

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 *)

Offset corrected by Reinhard Zumkeller, Nov 17 2015

A088765 a(n) = A087696(n)/2.

Original entry on oeis.org

4, 6, 9, 12, 18, 21, 24, 33, 39, 42, 51, 54, 66, 72, 81, 84, 93, 114, 117, 123, 138, 144, 156, 171, 177, 189, 192, 207, 213, 219, 222, 231, 252, 276, 291, 306, 318, 324, 339, 348, 357, 369, 378, 396, 408, 417, 429, 441, 462, 471, 486, 507, 513, 522, 528, 546

Offset: 1

Ray Chandler, Oct 26 2003

nonn

"Example 3: Ordinary twins 2a +- 1 for a = 2, 3, 6, 9, 15, . . . have D = 1 and are in class I. For D = 3, the twins 2a +- 3 occur for a = 4, 5, 7, 8, 10"; the latter is this sequence, from p. 3 of Weber. - Jonathan Vos Post, Feb 14 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..3100
H. J. Weber, Exceptional Prime Number Twins, Triplets and Multiplets, arXiv:1102.3075 [math.NT], 2011.

Cf. A087696, A040040, A088763, A088767, A088769.

[n/2: n in [3..2000] |IsPrime(n+5) and IsPrime(n-5)]; // Vincenzo Librandi, May 20 2017

Select[Range[3, 2000], PrimeQ[# + 5] && PrimeQ[# - 5] &] / 2 (* Vincenzo Librandi, May 20 2017 *)

Offset changed from 0 to 1 by Vincenzo Librandi, May 21 2017

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

Ray Chandler, Oct 26 2003

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..4350

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

[n/2: n in [5..1500] |IsPrime(n+9) and IsPrime(n-9)]; // Vincenzo Librandi, May 22 2017

Select[Range[5, 2000], PrimeQ[# + 9] && PrimeQ[# - 9] &] / 2 (* Vincenzo Librandi, May 21 2017 *)

cp's OEIS Frontend

A087697 Numbers k such that k + 7 and k - 7 are both prime.

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

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A088765 a(n) = A087696(n)/2.

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Magma

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Extensions

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

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Author

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Programs

Magma

Mathematica