A173286 2*prime(prime(prime(n)))-3 and 3*prime(prime(prime(n)))-2 are both primes.

1, 2, 5, 8, 9, 15, 26, 53, 63, 86, 92, 93, 95, 116, 137, 152, 233, 254, 281, 303, 329, 334, 352, 386, 392, 415, 423, 460, 470, 476, 508, 565, 570, 601, 660, 673, 680, 725, 748, 898, 907, 942, 948, 952, 958, 1045, 1119, 1126, 1138, 1140, 1259, 1314, 1360

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 15 2010

Keywords

• nonn

Examples

			a(1) = 1 because 2*p(p(p(1)))-3 = 7 = prime and 3*p(p(p(1)))-2 = 13 = prime;
a(2) = 2 because 2*p(p(p(2)))-3 = 19 = prime and 3*p(p(p(2)))-2 = 31 = prime;
a(3) = 5 because 2*p(p(p(5)))-3 = 379 = prime and 3*p(p(p(5)))-2 = 251 = prime;
a(4) = 8 because 2*p(p(p(8)))-3 = 991 = prime and 3*p(p(p(8)))-2 = 659 = prime;
a(5) = 9 because 2*p(p(p(9)))-3 = 1291 = prime and 3*p(p(p(9)))-2 = 859 = prime;
a(6) = 15 because 2*p(p(p(15)))-3 = 3889 = prime and 3*p(p(p(15)))-2 = 2591 = prime.
		

Crossrefs

Cf. A038580, A063908, A088878.

Programs

Mathematica

pppQ[n_]:=Module[{p=Prime[Prime[Prime[n]]]},AllTrue[{2p-3,3p-2},PrimeQ]]; Select[Range[1400],pppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 25 2016 *)

PARI

isok(n) = isprime(2*prime(prime(prime(n)))-3) && isprime(3*prime(prime(prime(n)))-2); \\ Michel Marcus, Sep 02 2013

Extensions

Extended beyond 15 by R. J. Mathar, Mar 01 2010