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.

Previous Showing 11-15 of 15 results.

A023259 Primes that remain prime through 2 iterations of function f(x) = 7x + 6.

Original entry on oeis.org

5, 11, 31, 59, 61, 71, 149, 179, 269, 439, 499, 541, 571, 719, 761, 1049, 1091, 1181, 1319, 1451, 1489, 1579, 1601, 1831, 1861, 1879, 1949, 2069, 2089, 2269, 2311, 2389, 2441, 2621, 2699, 2819, 2851, 2909, 3001, 3079, 3119, 3391, 3529, 3631, 3701, 3709
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 7*p+6 and 49*p+48 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023225, A024900. - John Cerkan, Sep 14 2016

Programs

  • Magma
    [n: n in [1..100000] | IsPrime(n) and IsPrime(7*n+6) and IsPrime(49*n+48)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Prime[Range[600]],AllTrue[Rest[NestList[7#+6&,#,2]],PrimeQ]&] (* Harvey P. Dale, Jan 26 2024 *)

Formula

a(n) = 1 or 9 (mod 10) for n > 1. - John Cerkan, Sep 14 2016

A164566 Primes p such that 7*p-6 and 7*p+6 are also prime numbers.

Original entry on oeis.org

5, 11, 19, 31, 41, 61, 71, 109, 151, 211, 229, 269, 379, 419, 431, 439, 479, 619, 641, 709, 739, 809, 839, 971, 1009, 1069, 1229, 1259, 1319, 1361, 1439, 1451, 1499, 1531, 1579, 1669, 1801, 1879, 1889, 2011, 2111, 2239, 2269, 2381, 2411, 2551, 2579, 2591
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Primes of the form A087681(k)/7, any index k.

Examples

			For p=5, both 7*5-6=29 and 7*5+6=41 are prime,
for p=11, both 7*11-6=71 and 7*11+6=83 are prime.

Links

Crossrefs

Cf. A106015, A125272, A127430, A046133, A087681, A136052, A023225.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) | IsPrime(7*p-6) and IsPrime(7*p+6)]; // Vincenzo Librandi, Apr 09 2013
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[7*p-6]&&PrimeQ[7*p+6],AppendTo[lst,p]], {n,6!}];lst
Select[Prime[Range[700]], And @@ PrimeQ/@{7 # + 6, 7 # - 6}&] (* Vincenzo Librandi, Apr 09 2013 *)
  • PARI
    is(n)=isprime(n) && isprime(7*n-6) && isprime(7*n+6) \\ Charles R Greathouse IV, Mar 28 2017

Formula

A136052 INTERSECT A023225. [R. J. Mathar, Aug 20 2009]

Extensions

Examples rephrased by R. J. Mathar, Aug 20 2009

A023290 Primes that remain prime through 3 iterations of function f(x) = 7x + 6.

Original entry on oeis.org

149, 439, 1319, 2069, 2089, 2389, 2699, 2819, 4259, 4919, 5059, 5689, 6469, 7559, 8429, 8669, 9199, 9239, 9319, 9769, 10159, 10529, 14449, 14479, 17659, 18899, 19289, 23879, 25189, 29819, 33119, 33149, 34159, 34439, 35089, 36229, 38839, 39829, 40699
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 7*p+6, 49*p+48 and 343*p+342 are primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023225, A023259, and A024900.

Programs

  • Magma
    [n: n in [1..150000] | IsPrime(n) and IsPrime(7*n+6) and IsPrime(49*n+48) and IsPrime(343*n+342)]; // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 9 (mod 10). - John Cerkan, Sep 23 2016

A023318 Primes that remain prime through 4 iterations of function f(x) = 7x + 6.

Original entry on oeis.org

1319, 2699, 4259, 4919, 5689, 8669, 10159, 10529, 29819, 33119, 82339, 86689, 98669, 174079, 177949, 196739, 207869, 210599, 222499, 231809, 253369, 267299, 275699, 323699, 362459, 371639, 378179, 388529, 397799, 402529, 421079, 448859, 468499
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 7*p+6, 49*p+48, 343*p+342 and 2401*p+2400 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023225, A023259, A023290, and A024900.

Programs

  • Magma
    [n: n in [1..1000000] | IsPrime(n) and IsPrime(7*n+6) and IsPrime(49*n+48) and IsPrime(343*n+342) and IsPrime(2401*n+2400)] // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 9 (mod 10). - John Cerkan, Oct 08 2016

A023346 Primes that remain prime through 5 iterations of function f(x) = 7x + 6.

Original entry on oeis.org

4259, 174079, 253369, 275699, 448859, 527159, 539639, 649969, 1101509, 1218559, 1230629, 1319729, 1426889, 1780939, 1929899, 1947109, 1960919, 2082469, 2087419, 2262409, 2479619, 2499169, 2797999, 2808359, 2809439, 2813339, 3089059, 3363749
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 7*p+6, 49*p+48, 343*p+342, 2401*p+2400 and 16807*p+16806 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023225, A023259, A023290, A023318, and A024900.

Programs

  • Magma
    [n: n in [1..10000000] | IsPrime(n) and IsPrime(7*n+6) and IsPrime(49*n+48) and IsPrime(343*n+342) and IsPrime(2401*n+2400) and IsPrime(16807*n+16806)] // Vincenzo Librandi, Aug 05 2010

Formula

a(n) == 9 (mod 10). - John Cerkan, Oct 24 2016
Previous Showing 11-15 of 15 results.

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

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