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A259730 Primes p such that both 2*p - 3 and 3*p - 2 are prime. 8
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 (list; graph; refs; listen; history; text; internal format)
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 A155916 A038979

Adjacent sequences:  A259727 A259728 A259729 * A259731 A259732 A259733

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 05 2015

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)