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

1,1

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

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 *)

Prog

(Haskell)
import Data.List.Ordered (isect)
a259730 n = a259730_list !! (n-1)
a259730_list = a063908_list `isect` a088878_list
(PARI) lista(nn) = forprime(p=3, nn, if(isprime(2*p-3) && isprime(3*p-2), print1(p, ", "))); \\ Altug Alkan, Jul 22 2017

Crossrefs

Intersection of A063908 and A088878; A172287, A259758.

Cf. A288814, A259758.

Sequence in context: A154319 A080114 A088878 * A254673 A343976 A155916

Adjacent sequences: A259727 A259728 A259729 * A259731 A259732 A259733

Keyword

nonn

Author

Reinhard Zumkeller, Jul 05 2015

Status

approved