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

1,2

Links

Table of n, a(n) for n=1..53.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A038580, A063908, A088878.

Sequence in context: A032684 A026448 A258353 * A243182 A088620 A068702

Adjacent sequences: A173283 A173284 A173285 * A173287 A173288 A173289

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 15 2010

Extensions

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

Status

approved