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A242262
Semiprimes of the form k^3 - 1.
3
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
1,1
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)
LINKS
FORMULA
a(n) = A096175(n-1)^3 - 1 for n > 1. - Jianing Song, Aug 01 2018
EXAMPLE
a(1) = 26 = 3^3 - 1 = 26 = 2 * 13, is a semiprime.
a(2) = 215 = 6^3 - 1 = 215 = 5 * 43, is a semiprime.
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 *)
CROSSREFS
Cf. A237040 (semiprimes of the form k^3 + 1).
Sequence in context: A213123 A125363 A126521 * A241938 A317865 A185553
KEYWORD
nonn
AUTHOR
K. D. Bajpai, May 09 2014
EXTENSIONS
First Mathematica program corrected by Harvey P. Dale, Jan 25 2019
STATUS
approved