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 1-2 of 2 results.

A290164 Primes p such that both 4*p - 3 and 3*p - 4 are prime.

Original entry on oeis.org

2, 5, 11, 19, 29, 59, 61, 79, 89, 131, 149, 151, 191, 389, 431, 479, 499, 521, 541, 571, 631, 659, 701, 739, 919, 941, 971, 1069, 1181, 1279, 1289, 1361, 1381, 1451, 1471, 1489, 1669, 1949, 2069, 2089, 2131, 2549, 2609, 2749, 2791, 3011, 3109, 3181, 3251, 3361
Offset: 1

Views

Author

David James Sycamore, Jul 22 2017

Keywords

Comments

For n >= 3, all terms end in 1 or 9. - Robert Israel, Jul 24 2017

Links

Crossrefs

Cf. A259730, A290163 (a subsequence).

Programs

  • Maple
    select(p -> isprime(p) and isprime(4*p-3) and isprime(3*p-4), [2,seq(i,i=3..10000,2)]); # Robert Israel, Jul 24 2017
  • Mathematica
    Select[Prime@ Range@ 500, Times @@ Boole@ Map[PrimeQ, {4 # - 3, 3 # - 4}] > 0 &] (* Michael De Vlieger, Jul 23 2017 *)
  • PARI
    forprime(p=2, 10000, if (isprime(3*p-4) && isprime(4*p-3), print1(p, ", "))) \\ Michel Marcus, Jul 23 2017

Extensions

More terms from Michel Marcus, Jul 23 2017

A289556 Primes p such that both 5*p - 4 and 4*p - 5 are prime.

Original entry on oeis.org

3, 7, 13, 43, 67, 109, 127, 151, 163, 211, 277, 307, 373, 457, 463, 601, 613, 673, 727, 853, 919, 967, 1021, 1117, 1171, 1231, 1399, 1471, 1483, 1747, 1789, 1933, 2029, 2251, 2311, 2389, 2503, 2521, 2557, 2659, 2851, 2857, 3019, 3067, 3121, 3229, 3583, 3613, 3637, 3691, 3697
Offset: 1

Views

Author

David James Sycamore, Aug 02 2017

Keywords

Comments

The terms of this sequence belong to two disjoint subsequences, namely those for which |A(5*p) - A(4*p)| = 9; (3,7,13,43,67,127,163,211,277,307,457,...), and those for which 5*A(4*p) - 3*A(5*p) = 3, (109,151,373,673,919,...), where A = A288814.
Note: A288814(n) = A056240(n) for all composite n.

Examples

			P=7: 5*7 - 4 = 31, 4*7 - 5 = 23, both prime so 7 is in this sequence, and belongs to the subsequence of terms satisfying A(4*p) - A(3*p) = 9.
P=109: 5*109 - 4 = 541, 4*109 - 5 = 431, both prime so 109 is in this sequence, and belongs to the subsequence of terms satisfying 5*A(4*p) - 3*A(5*p) = 3.

Crossrefs

Cf. A259730, A288814, A290163, A290164, A056240.
Intersection of A136051 and A156300. - Michel Marcus, Aug 04 2017

Programs

  • Mathematica
    Select[Prime@ Range@ 516, Times @@ Boole@ Map[PrimeQ, {5 # - 4, 4 # - 5}] > 0 &] (* Michael De Vlieger, Aug 02 2017 *)

Extensions

More terms from Altug Alkan, Aug 02 2017
Showing 1-2 of 2 results.

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

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