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.

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

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

A111250 Numbers n such that 7*n + 10 is prime.

Original entry on oeis.org

1, 3, 7, 9, 13, 21, 27, 31, 33, 37, 39, 43, 49, 51, 57, 67, 73, 79, 81, 87, 91, 93, 109, 111, 117, 121, 133, 139, 141, 147, 157, 159, 163, 169, 177, 181, 183, 187, 193, 207, 211, 219, 223, 229, 231, 237, 241, 249, 259, 267, 271, 277, 297, 303, 319, 333, 339, 343
Offset: 1

Views

Author

Parthasarathy Nambi, Oct 31 2005

Keywords

Comments

One less than the entry of A089033 at the same index.

Examples

			If n=117 then 7*n + 10 = 829 (prime).

Links

Crossrefs

Cf. A105772, A024902, A024900.

Programs

  • Magma
    [ n: n in [0..1500] | IsPrime(7*n + 10) ] // Vincenzo Librandi, Jan 31 2011
  • Mathematica
    Select[Range[400],PrimeQ[7#+10]&] (* Harvey P. Dale, Mar 25 2021 *)
  • PARI
    for(n=1,453,if(isprime(7*n + 10),print1(n,",")))

Extensions

Extended by Lambert Klasen (lambert.klasen(AT)gmx.net), Nov 02 2005

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

A111249 Numbers n such that 7*n + 8 is prime.

Original entry on oeis.org

3, 5, 9, 15, 17, 27, 29, 33, 39, 47, 53, 59, 63, 65, 69, 77, 87, 89, 93, 95, 99, 105, 107, 117, 125, 129, 135, 137, 143, 149, 155, 165, 183, 185, 195, 203, 209, 213, 225, 227, 237, 243, 245, 267, 275, 285, 287, 297, 303, 305, 315, 323, 327, 329, 333, 339, 345
Offset: 1

Views

Author

Parthasarathy Nambi, Oct 31 2005

Keywords

Comments

One less than the associated entry in A024905.

Examples

			If n=125 then 7*n + 8 = 883 (prime).

Crossrefs

Cf. A024900, A024902, A024905, A105772.

Programs

Showing 1-6 of 6 results.

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

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