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Numbers n such that n!-1 and n!+1 are both semiprime.
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%I #19 Aug 13 2023 12:02:11

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

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

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

%C a(11) >= 929. 929!-1 is semiprime, no factor of 929!+1 is known. - _Sean A. Irvine_, Mar 09 2013

%e 10!+1 = 3628801 = 11*329891 and 10!-1 = 3628799 = 29*125131 so 10 is a member of the sequence.

%e 464 is not a term since 464!-1=2828197538205421590987128183441789966021011*C996 is not a semiprime. - _Sean A. Irvine_, Mar 09 2013

%p 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;

%t 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 *)

%Y Cf. A078778, A078781.

%K hard,more,nonn

%O 1,1

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

%E a(10) from _D. S. McNeil_, Sep 04 2011