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 1-5 of 5 results.

A089144 Primes p such that 6*p-5 and 6*p-1 are primes.

Original entry on oeis.org

2, 3, 7, 17, 19, 47, 53, 59, 67, 103, 113, 127, 157, 239, 269, 283, 313, 379, 383, 397, 449, 467, 577, 613, 617, 647, 823, 829, 907, 929, 977, 1097, 1123, 1279, 1373, 1447, 1489, 1523, 1697, 1723, 1789, 1877, 1933, 2017, 2027, 2063, 2069, 2237, 2339, 2423
Offset: 1

Views

Author

Pierre CAMI, Dec 05 2003

Keywords

Examples

			6*7=42, 42-5=37, 42-1=41, 37 and 41 primes.

Links

Crossrefs

Cf. A090606, A090607, A090608, A090609, A090610.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) |IsPrime(6*p-5) and IsPrime(6*p-1)]; // Vincenzo Librandi, May 23 2017
  • Mathematica
    okQ[n_]:=Module[{x=6n},PrimeQ[x-1]&&PrimeQ[x-5]]; Select[Prime[Range[ 500]],okQ] (* Harvey P. Dale, May 25 2011 *)
Select[Prime[Range[400]], PrimeQ[6 # - 5] && PrimeQ[6 # - 1]&] (* Vincenzo Librandi, May 23 2017 *)

Extensions

More terms from Ray Chandler, Dec 06 2003

A090609 Primes of the form 6*p - 1 such that p and 6*p - 5 are primes.

Original entry on oeis.org

11, 17, 41, 101, 113, 281, 317, 353, 401, 617, 677, 761, 941, 1433, 1613, 1697, 1877, 2273, 2297, 2381, 2693, 2801, 3461, 3677, 3701, 3881, 4937, 4973, 5441, 5573, 5861, 6581, 6737, 7673, 8237, 8681, 8933, 9137, 10181, 10337, 10733, 11261, 11597, 12101
Offset: 1

Views

Author

Ray Chandler, Dec 06 2003

Keywords

Crossrefs

Cf. A089144, A090606, A090607, A090608, A090610.

Programs

  • Mathematica
    Select[6Prime[Range[300]]-1,PrimeQ[#]&&PrimeQ[#-4]&] (* Stefano Spezia, Feb 12 2025 *)
  • PARI
    lista(nn) = forprime(p=2, nn, if(isprime(6*p-1)&&isprime(6*p-5), print1(6*p-1, ", "))); \\ Jinyuan Wang, Aug 04 2021

Formula

a(n) = 6*A089144(n) - 1.

Extensions

Name clarified and offset changed to 1 by Jinyuan Wang, Aug 03 2021

A090606 A089144 indexed by A000040.

Original entry on oeis.org

1, 2, 4, 7, 8, 15, 16, 17, 19, 27, 30, 31, 37, 52, 57, 61, 65, 75, 76, 78, 87, 91, 106, 112, 113, 118, 143, 145, 155, 158, 165, 184, 188, 207, 220, 229, 237, 241, 265, 269, 278, 288, 295, 306, 307, 311, 312, 332, 346, 360, 368, 383, 388, 393, 404, 418, 439, 449
Offset: 1

Views

Author

Ray Chandler, Dec 06 2003

Keywords

Comments

Prime(k)*6 - 3 -+ 2 are both prime. - Juri-Stepan Gerasimov, Mar 19 2010

Crossrefs

Cf. A089144, A090607, A090608, A090609, A090610.

Formula

a(n)=k such that A000040(k)=A089144(n).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 03 2021

A090607 Primes of the form 6*p - 5 such that p and 6*p - 1 are primes.

Original entry on oeis.org

7, 13, 37, 97, 109, 277, 313, 349, 397, 613, 673, 757, 937, 1429, 1609, 1693, 1873, 2269, 2293, 2377, 2689, 2797, 3457, 3673, 3697, 3877, 4933, 4969, 5437, 5569, 5857, 6577, 6733, 7669, 8233, 8677, 8929, 9133, 10177, 10333, 10729, 11257, 11593, 12097
Offset: 1

Views

Author

Ray Chandler, Dec 06 2003

Keywords

Crossrefs

Cf. A089144, A090606, A090608, A090609, A090610.

Programs

  • PARI
    lista(nn) = forprime(p=2, nn, if(isprime(6*p-1)&&isprime(6*p-5), print1(6*p-5, ", "))); \\ Jinyuan Wang, Aug 04 2021

Formula

a(n) = 6*A089144(n) - 5.

Extensions

Name clarified by Jinyuan Wang, Aug 03 2021

A090610 A090609 indexed by A000040.

Original entry on oeis.org

5, 7, 13, 26, 30, 60, 66, 71, 79, 113, 123, 135, 160, 227, 255, 265, 288, 338, 342, 353, 392, 408, 484, 514, 517, 538, 660, 666, 719, 736, 771, 852, 869, 973, 1034, 1081, 1111, 1133, 1251, 1269, 1309, 1362, 1396, 1448, 1456, 1477, 1482, 1592, 1656, 1702, 1756
Offset: 1

Views

Author

Ray Chandler, Dec 06 2003

Keywords

Crossrefs

Cf. A089144, A090606, A090607, A090608, A090609.

Formula

a(n)=k such that A000040(k)=A090609(n).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 03 2021
Showing 1-5 of 5 results.

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

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