A257260 One-based position of the rightmost zero in the factorial base representation of n (A007623), 0 if no nonleading zeros present.

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

Offset

1,7

Comments

a(n) gives the distance of the rightmost zero from the right hand end of factorial base representation of n (A007623), particularly, 1 when n is even, and 0 for those cases when there are no nonleading zeros present (terms of A227157).

Sequence starts from n=1, to avoid ambiguities with case zero.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Index entries for sequences related to factorial base representation.

Example

For n = 1, with factorial base representation (A007623) "1", there are no nonleading zeros at all, thus a(1) = 0.
For n = 6, with representation "100", the rightmost zero occurs at digit-position 1 (when the least significant digit has index 1, etc.), thus a(6) = 1.
For n = 7, with representation "101", the rightmost zero occurs at position 2, thus a(7) = 2.

Mathematica

a[n_] := Module[{k = n, m = 2, r, s = {}, p}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; If[MissingQ[(p = FirstPosition[s, 0])], 0, p[[1]]]]; Array[a, 100] (* Amiram Eldar, Feb 07 2024 *)

Prog

(Scheme) (define (A257260 n) (let loop ((n n) (i 2)) (cond ((zero? n) 0) ((zero? (modulo n i)) (- i 1)) (else (loop (floor->exact (/ n i)) (+ 1 i))))))

Crossrefs

Cf. A007623, A227157 (positions of zeros), A000012 (even bisection).

Cf. also A257261, A230403, and arrays of permutations A060117 and A060118.

Sequence in context: A141095 A175599 A179759 * A334208 A159195 A265859

Adjacent sequences: A257257 A257258 A257259 * A257261 A257262 A257263

Keyword

nonn,base

Author

Antti Karttunen, Apr 29 2015

Status

approved