A241732 Primes p such that p^3 + 2 and p^3 - 2 are semiprime.

2, 11, 13, 17, 41, 89, 101, 239, 271, 331, 571, 641, 719, 1051, 1231, 1321, 1549, 1559, 1721, 1741, 1831, 1993, 1999, 2029, 2311, 2459, 2749, 2837, 2861, 2939, 3389, 3467, 3671, 4049, 4111, 4273, 4787, 4919, 4969, 5657, 5689, 5861, 6221, 6679, 6691, 6829, 7109

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..2310

Example

11 is prime and appears in the sequence because 11^3 + 2 = 1333 = 31 * 43 and 11^3 - 2 = 1329 = 3 * 443, both are semiprime.
41 is prime and appears in the sequence because 41^3 + 2 = 68923 = 157 * 439 and 41^3 - 2 = 68919 = 3 * 22973, both are semiprime.

Maple

with(numtheory): KD:= proc() local k; k:=ithprime(n); if bigomega(k^3+2)=2 and bigomega(k^3-2)=2 then k; fi; end: seq(KD(), n=1..2000);

Mathematica

A241732 = {}; Do[t = Prime[n]; If[PrimeOmega[t^3 + 2] == 2 && PrimeOmega[t^3 - 2] == 2, AppendTo[A241732, t]], {n, 500}]; A241732
Select[Prime[Range[1000]], PrimeOmega[#^3+2]==PrimeOmega[#^3-2]==2&] (* Harvey P. Dale, Jun 20 2019 *)

Crossrefs

Cf. A001358, A063637, A063638, A072381, A082919, A145292, A228183, A237627, A241483, A241493, A241659.

Sequence in context: A023257 A178796 A068807 * A154812 A038894 A207039

Adjacent sequences: A241729 A241730 A241731 * A241733 A241734 A241735

Keyword

nonn

Author

K. D. Bajpai, Apr 27 2014

Status

approved