A088763 -id:A088763 - cp's OEIS frontend

A087695 Numbers n such that n + 3 and n - 3 are both prime.

8, 10, 14, 16, 20, 26, 34, 40, 44, 50, 56, 64, 70, 76, 86, 100, 104, 106, 110, 134, 154, 160, 170, 176, 194, 196, 226, 230, 236, 254, 260, 266, 274, 280, 310, 314, 334, 350, 356, 370, 376, 386, 436, 446, 460, 464, 506, 544, 560, 566, 574, 590, 596

Offset: 1

Zak Seidov, Sep 27 2003

A010051(a(n)-3) * A010051(a(n)+3) = 1. - Reinhard Zumkeller, Nov 17 2015

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

Cf. A014574, A087678-A087683, A087696, A087697, A088763, A046117, A010051.

a087695 n = a087695_list !! (n-1)
a087695_list = filter
   (\x -> a010051' (x - 3) == 1 && a010051' (x + 3) == 1) [2, 4 ..]
-- Reinhard Zumkeller, Nov 17 2015

ZL:=[]:for p from 1 to 600 do if (isprime(p) and isprime(p+6) ) then ZL:=[op(ZL),(p+(p+6))/2]; fi; od; print(ZL); # Zerinvary Lajos, Mar 07 2007

lst={};Do[If[PrimeQ[n-3]&&PrimeQ[n+3], AppendTo[lst, n]], {n, 10^3}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)
Select[Range[600],AllTrue[#+{3,-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 06 2015 *)

p=2; q=3; forprime(r=5,1e3, if(q-p<7 && (q-p==6 || r-p==6), print1(p+3", ")); p=q; q=r) \\ Charles R Greathouse IV, May 22 2018

a(n) = A046117(n) - 3.

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

A260689 Table read by rows: numbers m such that (2n-m, 2n+m) is a prime pair.

Original entry on oeis.org

1, 1, 3, 5, 3, 7, 1, 5, 7, 3, 9, 3, 13, 1, 5, 11, 13, 3, 9, 17, 9, 15, 19, 5, 7, 13, 17, 19, 3, 15, 21, 9, 15, 25, 1, 7, 11, 13, 17, 23, 9, 15, 21, 27, 29, 3, 27, 5, 7, 17, 23, 25, 31, 9, 15, 21, 33, 35, 3, 21, 27, 33, 1, 5, 11, 19, 25, 29, 31, 37, 3, 15, 27

Offset: 2

Reinhard Zumkeller, Nov 17 2015

1 <= T(n,k) <= 2*n-3; T(n,2) > 3 for n > 3; all terms are odd;
A264526(n) = T(n,1);
A264527(n) = T(n,A069360(n));
T(A040040(n),1) = 1;
T(A088763(n),1) = 3.

			.   n | T(n,k)          | (2*n-T(n,k), 2*n+T(n,k))       k=1..A069360(n)
. ----+-----------------+-----------------------------------------------
.   2 | 1               | (3,5)
.   3 | 1               | (5,7)
.   4 | 3,5             | (5,11) (3,13)
.   5 | 3,7             | (7,13) (3,17)
.   6 | 1,5,7           | (11,13) (7,17) (5,19)
.   7 | 3,9             | (11,17) (5,23)
.   8 | 3,13            | (13,19) (3,29)
.   9 | 1,5,11,13       | (17,19) (13,23) (7,29) (5,31)
.  10 | 3,9,17          | (17,23) (11,29) (3,37)
.  11 | 9,15,19         | (13,31) (7,37) (3,41)
.  12 | 5,7,13,17,19    | (19,29) (17,31) (11,37) (7,41) (5,43)
.  13 | 3,15,21         | (23,29) (11,41) (5,47)
.  14 | 9,15,25         | (19,37) (13,43) (3,53)
.  15 | 1,7,11,13,17,23 | (29,31) (23,37) (19,41) (17,43) (13,47) (7,53)
.  16 | 9,15,21,27,29   | (23,41) (17,47) (11,53) (5,59) (3,61)
.  17 | 3,27            | (31,37) (7,61)
.  18 | 5,7,17,23,25,31 | (31,41) (29,43) (19,53) (13,59) (11,61) (5,67)
.  19 | 9,15,21,33,35   | (29,47) (23,53) (17,59) (5,71) (3,73)
.  20 | 3,21,27,33      | (37,43) (19,61) (13,67) (7,73) .

Reinhard Zumkeller, Rows n = 2..1000 of triangle, flattened
Index entries for sequences related to Goldbach conjecture

Cf. A069360 (row lengths), A010051, A264526, A264527.

a260689 n k = a260689_tabf !! (n-2) !! (k-1)
a260689_row n = [m | m <- [1, 3 .. 2 * n - 3],
                     a010051' (2*n + m) == 1, a010051' (2*n - m) == 1]
a260689_tabf = map a260689_row [2..]

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 *)

A264526 Smallest number m such that both 2n-m and 2n+m are primes.

Original entry on oeis.org

1, 1, 3, 3, 1, 3, 3, 1, 3, 9, 5, 3, 9, 1, 9, 3, 5, 9, 3, 1, 3, 15, 5, 3, 9, 7, 3, 15, 1, 9, 3, 5, 15, 3, 1, 15, 3, 5, 9, 15, 5, 3, 9, 7, 9, 15, 7, 9, 3, 1, 3, 3, 1, 3, 15, 13, 15, 9, 7, 9, 15, 13, 21, 21, 5, 3, 27, 1, 9, 15, 5, 33, 9, 1, 15, 3, 7, 9, 3, 5

Offset: 2

Reinhard Zumkeller, Nov 17 2015

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Cf. A014574, A040040, A082467, A088763, A260689, A264527.

Haskell
```
a264526 = head . a260689_row
```

snm[n_]:=Module[{m=1},While[!PrimeQ[2n-m]||!PrimeQ[2n+m],m=m+2];m]; Array[ snm,90,2] (* Harvey P. Dale, Aug 13 2017, optimized by Ivan N. Ianakiev, Mar 16 2018 *)

a(n) = {my(m=1); while(!(isprime(2*n-m) && isprime(2*n+m)), m+=2); m;} \\ Michel Marcus, Mar 18 2018

a(n) = A260689(n,1);
a(A040040(n)) = 1;
a(A014574(n)/2) = 1;
a(A088763(n)) = 3.
a(n) = A082467(2n). - Ivan N. Ianakiev, Oct 27 2021

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

Ray Chandler, Oct 26 2003

nonn

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

Cf. A087697, A040040, A088763, A088765, A088769.

Cf. A089192, A105760. [Vincenzo Librandi, Jan 18 2009]

cp's OEIS Frontend

A087695 Numbers n such that n + 3 and n - 3 are both prime.

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

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A260689 Table read by rows: numbers m such that (2*n-m, 2*n+m) is a prime pair.

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Haskell

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

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Programs

Magma

Mathematica

A264526 Smallest number m such that both 2*n-m and 2*n+m are primes.

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Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula

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

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Author

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Comments

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A260689 Table read by rows: numbers m such that (2n-m, 2n+m) is a prime pair.

A264526 Smallest number m such that both 2n-m and 2n+m are primes.