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

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Wikipedia, Factorial number system

Formula

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

Example

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

Crossrefs

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

Sequence in context: A069160 A089616 A089615 * A089731 A097098 A123679

Adjacent sequences: A301590 A301591 A301592 * A301594 A301595 A301596

Keyword

nonn

Author

Seiichi Manyama, Mar 24 2018

Status

approved