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

Author

Antti Karttunen, Apr 29 2015

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Index entries for sequences related to factorial base representation.

Crossrefs

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

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

Programs

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 *)

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))))))