A242262 Semiprimes of the form k^3 - 1.

26, 215, 511, 1727, 2743, 7999, 13823, 54871, 157463, 238327, 511999, 728999, 1330999, 2628071, 3374999, 4410943, 4741631, 7077887, 7301383, 20123647, 21484951, 30959143, 36594367, 42144191, 63044791, 64964807, 81746503, 124999999, 187149247, 264609287, 267089983

Offset: 1

Author

K. D. Bajpai, May 09 2014

Keywords

• nonn

Comments

From Jianing Song, Aug 01 2018: (Start)

k^3 - 1 is a term iff k - 1 and k^2 + k + 1 are both prime.

Is this sequence infinite? That is, are there infinitely many primes p such that p^2 + 3*p + 3 is also prime?

(End)

Examples

			a(1) = 26 = 3^3 - 1 = 26 = 2 * 13, is a semiprime.
a(2) = 215 = 6^3 - 1 = 215 = 5 * 43, is a semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..2474

Crossrefs

Cf. A001358, A096175.

Cf. A237040 (semiprimes of the form k^3 + 1).

Programs

Maple

with(numtheory): A242262:= proc() local k; k:= x^3-1; if bigomega(k) = 2  then RETURN (k); fi; end: seq(A242262 (),x=1..1000);

Mathematica

Select[Table[n^3 - 1, {n, 100}], PrimeOmega[#] == 2 &]
Select[Range[700]^3-1,PrimeOmega[#]==2&] (* Harvey P. Dale, Jan 25 2019 *)

Formula

a(n) = A096175(n-1)^3 - 1 for n > 1. - Jianing Song, Aug 01 2018

Extensions

First Mathematica program corrected by Harvey P. Dale, Jan 25 2019