login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

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

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. A001358, A096175.

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

Sequence in context: A213123 A125363 A126521 * A241938 A317865 A185553

Adjacent sequences:  A242259 A242260 A242261 * A242263 A242264 A242265

KEYWORD

nonn

AUTHOR

K. D. Bajpai, May 09 2014

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 2 10:07 EDT 2022. Contains 355004 sequences. (Running on oeis4.)