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.

A125822 Numbers k for which 8*k + 1 and 8*k + 3 are twin primes.

Original entry on oeis.org

2, 5, 17, 35, 65, 71, 77, 80, 101, 107, 110, 131, 161, 185, 212, 215, 260, 266, 332, 341, 350, 371, 407, 416, 491, 500, 506, 527, 530, 542, 560, 581, 590, 626, 677, 680, 707, 731, 761, 806, 821, 836, 845, 932
Offset: 1

Views

Author

Artur Jasinski, Dec 10 2006

Keywords

Links

Crossrefs

Cf. A001109, A125821.

Programs

  • Mathematica
    Do[If[PrimeQ[8n + 1] && PrimeQ[8n + 3], Print[n]], {n, 1, 1000}]
Select[Range[1000],AllTrue[8#+{1,3},PrimeQ]&] (* Harvey P. Dale, Jul 11 2023 *)

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

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

A124192 Numbers k for which 8*k + 3 and 8*k + 5 are twin primes.

Original entry on oeis.org

0, 1, 7, 13, 22, 28, 43, 52, 82, 103, 127, 136, 178, 181, 202, 208, 223, 241, 253, 283, 292, 406, 412, 421, 433, 442, 481, 502, 511, 532, 568, 598, 616, 637, 706, 733, 766, 787, 832, 847, 853, 868, 901, 913, 916, 943
Offset: 1

Views

Author

Artur Jasinski, Dec 10 2006

Keywords

Examples

			0 is a term since 8*0 + 3 = 3 and 8*0 + 5 = 5 are twin primes.

Links

Crossrefs

Cf. A001109, A125821, A125822.

Programs

  • Magma
    [k:k in [0..1000]|IsPrime(8*k+3) and IsPrime(8*k+5)]; // Marius A. Burtea, Dec 19 2019
  • Mathematica
    Do[If[PrimeQ[8n + 3] && PrimeQ[8n + 5], Print[n]], {n, 1, 1000}]

Extensions

a(1) inserted by Amiram Eldar, Dec 19 2019

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 *)
Showing 1-6 of 6 results.

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