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

0,9

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.

Links

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

Formula

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

Example

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.

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 *)

Prog

(Scheme) (define (A257687 n) (- n (A257686 n)))
(Python)
from sympy import factorial as f
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def a(n):
    x=str(a007623(n))[1:][::-1]
    return sum(int(x[i])*f(i + 1) for i in range(len(x)))
print([a(n) for n in range(201)]) # Indranil Ghosh, Jun 21 2017

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.

Sequence in context: A049265 A010875 A260187 * A309957 A365459 A220660

Adjacent sequences: A257684 A257685 A257686 * A257688 A257689 A257690

Keyword

nonn,base

Author

Antti Karttunen, May 04 2015

Status

approved