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

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

1,1

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.

Links

Table of n, a(n) for n=1..51.

Example

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.

Mathematica

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

Crossrefs

Cf. A259730, A288814, A290163, A290164, A056240.

Intersection of A136051 and A156300. - Michel Marcus, Aug 04 2017

Sequence in context: A062605 A191974 A174241 * A086208 A090968 A020641

Adjacent sequences: A289553 A289554 A289555 * A289557 A289558 A289559

Keyword

nonn

Author

David James Sycamore, Aug 02 2017

Extensions

More terms from Altug Alkan, Aug 02 2017

Status

approved