cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A242262 Semiprimes of the form k^3 - 1.

This page as a plain text file.
%I A242262 #19 Jan 25 2019 17:28:33
%S A242262 26,215,511,1727,2743,7999,13823,54871,157463,238327,511999,728999,
%T A242262 1330999,2628071,3374999,4410943,4741631,7077887,7301383,20123647,
%U A242262 21484951,30959143,36594367,42144191,63044791,64964807,81746503,124999999,187149247,264609287,267089983
%N A242262 Semiprimes of the form k^3 - 1.
%C A242262 From _Jianing Song_, Aug 01 2018: (Start)
%C A242262 k^3 - 1 is a term iff k - 1 and k^2 + k + 1 are both prime.
%C A242262 Is this sequence infinite? That is, are there infinitely many primes p such that p^2 + 3*p + 3 is also prime?
%C A242262 (End)
%H A242262 K. D. Bajpai, <a href="/A242262/b242262.txt">Table of n, a(n) for n = 1..2474</a>
%F A242262 a(n) = A096175(n-1)^3 - 1 for n > 1. - _Jianing Song_, Aug 01 2018
%e A242262 a(1) = 26 = 3^3 - 1 = 26 = 2 * 13, is a semiprime.
%e A242262 a(2) = 215 = 6^3 - 1 = 215 = 5 * 43, is a semiprime.
%p A242262 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 A242262 Select[Table[n^3 - 1, {n, 100}], PrimeOmega[#] == 2 &]
%t A242262 Select[Range[700]^3-1,PrimeOmega[#]==2&] (* _Harvey P. Dale_, Jan 25 2019 *)
%Y A242262 Cf. A001358, A096175.
%Y A242262 Cf. A237040 (semiprimes of the form k^3 + 1).
%K A242262 nonn
%O A242262 1,1
%A A242262 _K. D. Bajpai_, May 09 2014
%E A242262 First Mathematica program corrected by _Harvey P. Dale_, Jan 25 2019