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%I #33 Mar 26 2018 19:56:42
%S 1,1,2,0,0,1,2,2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,3,0,0,2,3,3,4,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N n can be represented the sum of a(n) distinct factorials. (If there is no such representation, a(n) = 0.)
%H Seiichi Manyama, <a href="/A301593/b301593.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Factoradic">Factorial number system</a>
%F a(n!) = 1, a(n!+1) = 2.
%e n | | a(n)
%e --+------------------------+-----
%e 1 | 1! | 1
%e 2 | 2! | 1
%e 3 | 1! + 2! | 2
%e 6 | 3! | 1
%e 7 | 3! + 1! | 2
%e 8 | 3! + 2! | 2
%e 9 | 3! + 2! + 1! | 3
%Y Cf. A000142, A007489, A038507, A059590, A108731, A115944, A301523.
%K nonn
%O 1,3
%A _Seiichi Manyama_, Mar 24 2018
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