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A098594
Numbers n such that n!-1 and n!+1 are both semiprime.
0
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
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
Sequence in context: A256360 A205676 A352676 * A154315 A182084 A262707
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