A265893 a(n) = A084558(n) - A230403(n); the length of factorial base representation of n without its trailing zeros.

0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 1, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 1

Offset: 0

Author

Antti Karttunen, Dec 20 2015

Keywords

• nonn
• base

Examples

			In factorial base A007623, 0 is shown as "0", but in this case all the zeros are trailing, so we set a(0) = 0 by convention.
For n = 2, A007623(2) = "10", and by discarding the trailing zero only one significant digit "1" is left, thus a(2) = 1.
For n = 132, A007623(132) = "10200", and by discarding its trailing zeros we are left with just three digits "102", thus a(132) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A007623, A084558, A230403.

Column 1 of A265892.

Programs

Mathematica

a[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; Length[s] - FirstPosition[s, ?(#>0 &)][[1]] + 1]; a[0] = 0; Array[a, 100, 0] (* _Amiram Eldar, Feb 21 2024 *)

Scheme

(define (A265893 n) (- (A084558 n) (A230403 n)))

Formula

a(n) = A084558(n) - A230403(n).