A257261 One-based position of the rightmost one in the factorial base representation (A007623) of n, 0 if no one is present.

0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 4, 1, 2, 1, 4, 1, 3, 1, 2, 1, 3, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 1, 4, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 5

Offset: 0

Author

Antti Karttunen, Apr 29 2015

Keywords

• nonn
• base

Examples

			For n = 0, with factorial base representation (A007623) "0", there are no ones present at all, thus a(0) = 0.
For n = 1, with representation "1", the rightmost one occurs at digit-position 1 (when the least significant digit has index 1, etc.), thus a(1) = 1.
For n = 6, with representation "100", the rightmost one occurs at position 3, thus a(6) = 3.
For n = 11, with representation "121", the rightmost one occurs at digit-position 1 (when the least significant digit has index 1, etc.), thus a(11) = 1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10081
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A007623, A257260.

Cf. A000142 (positions of records, where each n first occurs as a value), A255411 (positions of zeros), A000012 (odd bisection).

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, 1])], 0, p[[1]]]]; Array[a, 100, 0] (* Amiram Eldar, Feb 07 2024 *)

Scheme

(define (A257261 n) (let loop ((n n) (i 2)) (cond ((zero? n) 0) ((= 1 (modulo n i)) (- i 1)) (else (loop (floor->exact (/ n i)) (+ 1 i))))))

Formula

Other identities:

For all n >= 1, a(n!) = n.