A259730 Primes p such that both 2*p - 3 and 3*p - 2 are prime.

3, 5, 7, 11, 13, 23, 37, 43, 53, 67, 71, 113, 127, 137, 167, 181, 191, 193, 211, 251, 263, 331, 347, 373, 431, 433, 443, 461, 487, 587, 727, 751, 757, 907, 991, 1021, 1091, 1103, 1171, 1187, 1213, 1231, 1297, 1367, 1453, 1483, 1597, 1637, 1663, 1667, 1733

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2015

Keywords

• nonn

Comments

A010051(2*a(n) - 3) * A010051(3*a(n) - 2) = 1;

A259758(n) = (2*a(n) - 3) * (3*a(n) - 2).

Except for a(1)=3 this is the same sequence as primes p such that A288814(3*p) - A288814(2*p) = 5. - David James Sycamore, Jul 22 2017

Furthermore, (A288814(3*p)*A288814(2*p))/6 belongs to A259758. - David James Sycamore, Jul 23 2017

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A063908 and A088878; A172287, A259758.

Cf. A288814, A259758.

Programs

Haskell

import Data.List.Ordered (isect)
a259730 n = a259730_list !! (n-1)
a259730_list = a063908_list `isect` a088878_list

Mathematica

Select[Prime@ Range@ 270, Times @@ Boole@ Map[PrimeQ, {2 # - 3, 3 # - 2}] > 0 &] (* Michael De Vlieger, Jul 22 2017 *)
Select[Prime[Range[300]],AllTrue[{2#-3,3#-2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 08 2020 *)

PARI

lista(nn) = forprime(p=3, nn, if(isprime(2*p-3) && isprime(3*p-2), print1(p, ", "))); \\ Altug Alkan, Jul 22 2017