A242262 - OEIS

%I #19 Jan 25 2019 17:28:33

%S 26,215,511,1727,2743,7999,13823,54871,157463,238327,511999,728999,

%T 1330999,2628071,3374999,4410943,4741631,7077887,7301383,20123647,

%U 21484951,30959143,36594367,42144191,63044791,64964807,81746503,124999999,187149247,264609287,267089983

%N Semiprimes of the form k^3 - 1.

%C From _Jianing Song_, Aug 01 2018: (Start)

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

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

%C (End)

%H K. D. Bajpai, <a href="/A242262/b242262.txt">Table of n, a(n) for n = 1..2474</a>

%F a(n) = A096175(n-1)^3 - 1 for n > 1. - _Jianing Song_, Aug 01 2018

%e a(1) = 26 = 3^3 - 1 = 26 = 2 * 13, is a semiprime.

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

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

%t Select[Table[n^3 - 1, {n, 100}], PrimeOmega[#] == 2 &]

%t Select[Range[700]^3-1,PrimeOmega[#]==2&] (* _Harvey P. Dale_, Jan 25 2019 *)

%Y Cf. A001358, A096175.

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

%K nonn

%O 1,1

%A _K. D. Bajpai_, May 09 2014

%E First Mathematica program corrected by _Harvey P. Dale_, Jan 25 2019