Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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