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

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..10080

Index entries for sequences related to factorial base representation.

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A007623, A084558, A230403.

Column 1 of A265892.

Sequence in context: A143773 A323524 A354713 * A191372 A185316 A053279

Adjacent sequences: A265890 A265891 A265892 * A265894 A265895 A265896

Keyword

nonn,base

Author

Antti Karttunen, Dec 20 2015

Status

approved