OFFSET
1,1
COMMENTS
a(n) == 3 (mod 4) for n > 3.
EXAMPLE
a(5) = 135 because 135 - 1! = 134 = 2*67, 135 - 2! = 133 = 7 * 19, 135 - 3! = 129 = 3 * 43, 135 - 4! = 111 = 3 * 39 and 135 - 5! = 15 = 3 * 5 are all semiprimes, and no number smaller than 135 works.
MAPLE
f:= proc(n) local F, k, i;
F:= [seq(i!, i=1..n)];
for k from n! + 4 do
if andmap(t -> numtheory:-bigomega(k-t) = 2, F) then return k fi
od
end proc:
map(f, [$1..13]);
MATHEMATICA
a[n_]:=Module[{k=n!+1}, While[Product[Boole[PrimeOmega[k-i!]==2], {i, n}]!=1, k++]; k]; Array[a, 9] (* Stefano Spezia, Sep 20 2024 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert Israel, Sep 20 2024
STATUS
approved