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

Author

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

Keywords

• hard
• more
• nonn

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

Examples

			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
		

Crossrefs

Cf. A078778, A078781.

Programs

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 *)

Extensions

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