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

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..10081

Index entries for sequences related to factorial base representation.

Formula

Other identities:

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

Example

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.

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 *)

Prog

(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))))))

Crossrefs

Cf. A007623, A257260.

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

Sequence in context: A297325 A375466 A278528 * A355141 A171963 A357928

Adjacent sequences: A257258 A257259 A257260 * A257262 A257263 A257264

Keyword

nonn,base

Author

Antti Karttunen, Apr 29 2015

Status

approved