A257687 Discard the most significant digit from factorial base representation of n, then convert back to decimal: a(n) = n - A257686(n).

0, 0, 0, 1, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0

Offset: 0

Author

Antti Karttunen, May 04 2015

Keywords

• nonn
• base

Comments

A060130(n) gives the number of steps needed to reach zero, when starting iterating as a(k), a(a(k)), etc., from the starting value k = n.

Examples

			Factorial base representation (A007623) of 1 is "1", discarding the most significant digit leaves nothing, taken to be zero, thus a(1) = 0.
Factorial base representation of 2 is "10", discarding the most significant digit leaves "0", thus a(2) = 0.
Factorial base representation of 3 is "11", discarding the most significant digit leaves "1", thus a(3) = 1.
Factorial base representation of 4 is "20", discarding the most significant digit leaves "0", thus a(4) = 0.
		

Links

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

Crossrefs

Cf. A007623, A257686.

Can be used (together with A099563) to define simple recurrences for sequences like A034968, A060130, A227153, A246359, A257511, A257679, A257680.

Cf. also A257684.

Programs

Mathematica

f[n_] := Block[{m = p = 1}, While[p*(m + 1) <= n, p = p*m; m++]; Mod[n, p]]; Array[f, 101, 0] (* Robert G. Wilson v, Jul 21 2015 *)

Python

from sympy import factorial as f
def a007623(n, p=2): return n if n
Indranil Ghosh, Jun 21 2017

Scheme

(define (A257687 n) (- n (A257686 n)))

Formula

a(n) = n - A257686(n).