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A289556 Primes p such that both 5*p - 4 and 4*p - 5 are prime. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 12:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)