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.

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

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

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

A090608 A090607 indexed by A000040.

Original entry on oeis.org

4, 6, 12, 25, 29, 59, 65, 70, 78, 112, 122, 134, 159, 226, 254, 264, 287, 337, 341, 352, 391, 407, 483, 513, 516, 537, 659, 665, 718, 735, 770, 851, 868, 972, 1033, 1080, 1110, 1132, 1250, 1268, 1308, 1361, 1395, 1447, 1455, 1476, 1481, 1591, 1655, 1701, 1755
Offset: 1

Views

Author

Ray Chandler, Dec 06 2003

Keywords

Crossrefs

Cf. A089144, A090606, A090607, A090609, A090610.

Formula

a(n)=k such that A000040(k)=A090607(n).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 03 2021

A162565 Those primes p such that (p-q) divides (p-1), where q is the greatest prime < p.

Original entry on oeis.org

3, 5, 7, 13, 17, 19, 31, 37, 41, 43, 61, 67, 73, 79, 97, 101, 103, 109, 113, 127, 139, 151, 157, 163, 181, 191, 193, 197, 199, 229, 233, 241, 251, 271, 277, 281, 283, 313, 317, 337, 349, 353, 373, 379, 401, 409, 421, 431, 433, 439, 457, 461, 463, 523, 541, 547
Offset: 1

Views

Author

Leroy Quet, Jul 06 2009

Keywords

Comments

A006512 (greater of twin primes) is a subsequence. - Michel Marcus, Feb 27 2019
Except for 11, A090609 is a subsequence. - Davide Rotondo, Feb 12 2025

Examples

			The 17th prime is 59 and the 18th prime is 61. (61-59) = 2, and 2 divides 61-1 = 60. So 61 is in the sequence.

Links

Crossrefs

Cf. A006512, A162566.

Programs

  • Maple
    A162565 := proc(n) local p,q; p := ithprime(n) ; q := prevprime(p) ; if (p-1) mod (p-q) = 0 then printf("%d,",p); fi; end: seq(A162565(n),n=2..200) ; # R. J. Mathar, Jul 13 2009
  • Mathematica
    Transpose[Select[Partition[Prime[Range[110]],2,1],Divisible[#[[2]]-1, #[[2]] - #[[1]]]&]][[2]] (* Harvey P. Dale, Mar 18 2016 *)
  • PARI
    isok(p) = isprime(p) && !((p-1) % (p-precprime(p-1))); \\ Michel Marcus, Feb 12 2025

Extensions

More primes from R. J. Mathar, Jul 13 2009
Showing 1-6 of 6 results.

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