A098594 Numbers n such that n!-1 and n!+1 are both semiprime.

5, 8, 10, 13, 20, 24, 26, 34, 59, 392

Offset

1,1

Comments

This sequence is formed of all those terms that appear in both A078778 and A078781.

a(11) >= 929. 929!-1 is semiprime, no factor of 929!+1 is known. - Sean A. Irvine, Mar 09 2013

Links

Table of n, a(n) for n=1..10.

Example

10!+1 = 3628801 = 11*329891 and 10!-1 = 3628799 = 29*125131 so 10 is a member of the sequence.
464 is not a term since 464!-1=2828197538205421590987128183441789966021011*C996 is not a semiprime. - Sean A. Irvine, Mar 09 2013

Maple

out:=[]: for n from 1 to 60 do: a:=n!-1: b:=n!+1: if (bigomega(a)=2) and (bigomega(b)=2) then out:=[op(out), n]: print(n): fi: od: out;

Mathematica

Select[Range[35], PrimeOmega[#!+{1, -1}]=={2, 2}&] (* The program generates the first 8 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Aug 13 2023 *)

Crossrefs

Cf. A078778, A078781.

Sequence in context: A256360 A205676 A352676 * A154315 A182084 A262707

Adjacent sequences: A098591 A098592 A098593 * A098595 A098596 A098597

Keyword

hard,more,nonn

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 17 2004

Extensions

a(10) from D. S. McNeil, Sep 04 2011

Status

approved