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.

A139404 Numbers k such that 24*k + 5 and 24*k + 7 are twin primes.

Original entry on oeis.org

0, 1, 4, 6, 8, 11, 19, 34, 44, 51, 53, 54, 78, 81, 83, 89, 93, 96, 99, 106, 116, 141, 144, 148, 149, 159, 163, 173, 176, 184, 188, 193, 209, 228, 229, 239, 258, 261, 279, 286, 306, 316, 323, 328, 331, 351, 358, 368, 369, 389, 393, 394, 401, 403, 418, 429, 446
Offset: 1

Views

Author

Artur Jasinski, Apr 19 2008

Keywords

Comments

1/3 of number k such that 8k + 5 and 8k + 7 are primes.
All numbers in A125821 are divisible by 3.

Examples

			0 is in the sequence since 24*0 + 5 = 5 and 24*0 + 7 = 7 are twin primes.

Links

Crossrefs

Cf. A125822, A139402, A139404.

Programs

  • Magma
    [n: n in [0..5000] |IsPrime(24*n+5)and IsPrime(24*n+7)]; // Vincenzo Librandi, Nov 24 2010
  • Mathematica
    a = {}; Do[If[PrimeQ[8 n + 5] && PrimeQ[8 n + 3] && PrimeQ[n],AppendTo[a, n]], {n, 1, 10000}]; a
Select[Range[0,500],AllTrue[24#+{5,7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 08 2019 *)

Formula

a(n) = A125821(n)/3.

Extensions

a(1) = 0 inserted by Vincenzo Librandi, Mar 25 2010

A125821 Numbers k for which 8*k+5 and 8*k+7 are twin primes.

Original entry on oeis.org

3, 12, 18, 24, 33, 57, 102, 132, 153, 159, 162, 234, 243, 249, 267, 279, 288, 297, 318, 348, 423, 432, 444, 447, 477, 489, 519, 528, 552, 564, 579, 627, 684, 687, 717, 774, 783, 837, 858, 918, 948, 969, 984, 993
Offset: 1

Views

Author

Artur Jasinski, Dec 10 2006

Keywords

Comments

From Zak Seidov, Apr 19 2008: (Start)
Proof that all numbers in this sequence are divisible by 3:
if n=(3k+1), then 8n+7=8(3k+1)+7=3(5+8 k) (composite)
if n=(3k+2), then 8n+5=8(3k+2)+5=3(7+8 k) (composite),
so if we require that both 8n+5 and 8n+7 are primes, then n=3k, hence all terms in this sequence are multiples of 3. QED. (End)

Links

Crossrefs

Cf. A001109.
For a(n)/3 see A139404.
Cf. A125822, A139402, A139404.

Programs

  • Mathematica
    Do[If[PrimeQ[8n + 5] && PrimeQ[8n + 7], Print[n]], {n, 1, 1000}]
Select[Range[3,6000,3],AllTrue[8#+{5,7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 14 2018 *)

A139405 Numbers k such that 8*k+1 and 8*k+7 are primes.

Original entry on oeis.org

2, 5, 9, 12, 24, 29, 32, 44, 54, 57, 74, 75, 80, 107, 110, 122, 129, 137, 152, 162, 165, 170, 179, 185, 194, 200, 207, 219, 222, 234, 249, 260, 267, 285, 297, 299, 302, 305, 332, 339, 362, 414, 432, 452, 470, 500, 509, 519, 555, 557, 564, 570, 582, 584, 599
Offset: 1

Views

Author

Artur Jasinski, Apr 19 2008

Keywords

Links

Crossrefs

Cf. A017077, A004771.
Cf. A125821, A125822, A139402, A139404.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[8 n + 1] && PrimeQ[8 n + 7], AppendTo[a, n]], {n, 1, 1000}]; a

A139406 Numbers k such that 8*k+1 and 8*k+5 are primes.

Original entry on oeis.org

12, 24, 39, 57, 84, 96, 117, 126, 162, 186, 201, 234, 249, 267, 297, 309, 327, 336, 354, 357, 369, 402, 432, 441, 459, 462, 474, 516, 519, 564, 591, 621, 654, 696, 711, 717, 732, 777, 822, 942, 969, 984, 1011, 1029, 1086, 1092, 1116, 1167, 1179, 1272, 1341
Offset: 1

Views

Author

Artur Jasinski, Apr 19 2008

Keywords

Links

Crossrefs

Cf. A125821, A125822, A139402, A139404, A139405, A139407.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[8 n + 1] && PrimeQ[8 n + 5], AppendTo[a, n]], {n, 1, 1000}]; a
Select[Range[1500],And@@PrimeQ[8 #+{1,5}]&] (* Harvey P. Dale, Aug 14 2011 *)

A139407 Numbers k such that 8*k+3 and 8*k+7 are primes.

Original entry on oeis.org

2, 5, 8, 20, 38, 47, 62, 80, 92, 107, 110, 113, 185, 197, 233, 260, 275, 293, 317, 332, 335, 338, 377, 395, 398, 488, 500, 653, 668, 722, 740, 755, 818, 863, 905, 950, 962, 965, 1052, 1055, 1067, 1097, 1100, 1193, 1202, 1217, 1223, 1235, 1262, 1280, 1283
Offset: 1

Views

Author

Artur Jasinski, Apr 19 2008

Keywords

Links

Crossrefs

Cf. A125821, A125822, A139402, A139404, A139405, A139406.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[8 n + 3] && PrimeQ[8 n + 7], AppendTo[a, n]], {n, 1, 1000}]; a
Select[Range[1500],And@@PrimeQ[8 # +{3,7}]&] (* Harvey P. Dale, Mar 24 2011 *)

A139403 Prime numbers k such that 8*k+3 and 8*k+5 are also primes.

Original entry on oeis.org

7, 13, 43, 103, 127, 181, 223, 241, 283, 421, 433, 733, 787, 853, 1291, 1303, 1531, 1567, 1741, 2017, 2161, 2281, 2593, 2857, 2953, 3163, 3361, 3571, 3673, 4003, 4051, 4441, 4513, 4597, 4663, 4831, 4903, 5503, 5647, 5923, 6067, 6091, 6217, 6361, 6427
Offset: 1

Views

Author

Artur Jasinski, Apr 19 2008

Keywords

Links

Crossrefs

Cf. A125822, A139402, A139404.
Subsequence of prime terms of A124192.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[8 n + 5] && PrimeQ[8 n + 3] && PrimeQ[n],AppendTo[a, n]], {n, 1, 10000}]; a
Select[Prime[Range[1000]],AllTrue[8#+{3,5},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 30 2020 *)
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.