A301593 n can be represented the sum of a(n) distinct factorials. (If there is no such representation, a(n) = 0.)

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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Seiichi Manyama, Mar 24 2018

Keywords

• nonn

Examples

			n |                        | a(n)
--+------------------------+-----
1 | 1!                     |  1
2 | 2!                     |  1
3 | 1! + 2!                |  2
6 | 3!                     |  1
7 | 3! + 1!                |  2
8 | 3! + 2!                |  2
9 | 3! + 2! + 1!           |  3
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• Wikipedia, Factorial number system

Crossrefs

Cf. A000142, A007489, A038507, A059590, A108731, A115944, A301523.

Formula

a(n!) = 1, a(n!+1) = 2.