A259730 - OEIS

%I #26 Mar 08 2020 16:35:21

%S 3,5,7,11,13,23,37,43,53,67,71,113,127,137,167,181,191,193,211,251,

%T 263,331,347,373,431,433,443,461,487,587,727,751,757,907,991,1021,

%U 1091,1103,1171,1187,1213,1231,1297,1367,1453,1483,1597,1637,1663,1667,1733

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

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

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

%C 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

%C Furthermore, (A288814(3*p)*A288814(2*p))/6 belongs to A259758. - _David James Sycamore_, Jul 23 2017

%H Reinhard Zumkeller, <a href="/A259730/b259730.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Prime@ Range@ 270, Times @@ Boole@ Map[PrimeQ, {2 # - 3, 3 # - 2}] > 0 &] (* _Michael De Vlieger_, Jul 22 2017 *)

%t 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 *)

%o (Haskell)

%o import Data.List.Ordered (isect)

%o a259730 n = a259730_list !! (n-1)

%o a259730_list = a063908_list `isect` a088878_list

%o (PARI) lista(nn) = forprime(p=3, nn, if(isprime(2*p-3) && isprime(3*p-2), print1(p, ", "))); \\ _Altug Alkan_, Jul 22 2017

%Y Intersection of A063908 and A088878; A172287, A259758.

%Y Cf. A288814, A259758.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 05 2015