A276009 Decrement each nonzero digit by one in factorial base representation of n: a(n) = n - A276008(n).

0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 6, 6, 6, 6, 8, 8, 12, 12, 12, 12, 14, 14, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 6, 6, 6, 6, 8, 8, 12, 12, 12, 12, 14, 14, 24, 24, 24, 24, 26, 26, 24, 24, 24, 24, 26, 26, 30, 30, 30, 30, 32, 32, 36, 36, 36, 36, 38, 38, 48, 48, 48, 48, 50, 50, 48, 48, 48, 48, 50, 50, 54, 54, 54, 54, 56, 56, 60, 60, 60, 60, 62, 62, 72, 72, 72, 72

Offset

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..40320

Index entries for sequences related to factorial base representation.

Formula

a(n) = n - A276008(n).

Example

For n=23 whose factorial base representation is "321", when we subtract one from each digit we get "210", the factorial base representation of 14, thus a(23) = 14.
For n=37 ("1201"), when we subtract one from each digit we get "0100", thus a(37) = 6 as A007623(6) = 100.

Mathematica

a[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; s = Max[# - 1, 0]& /@ s; Total[s*Range[Length[s]]!]]; Array[a, 100, 0] (* Amiram Eldar, Feb 14 2024 *)

Prog

(Scheme)
(define (A276009 n) (- n (A276008 n)))
;; Standalone version:
(define (A276009 n) (let loop ((n n) (s 0) (f 1) (i 2)) (if (zero? n) s (let ((d (modulo n i))) (if (zero? d) (loop (/ n i) s (* i f) (+ 1 i)) (loop (/ (- n d) i) (+ s (* f (- d 1))) (* i f) (+ 1 i)))))))
(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))
    y="".join(str(int(i) - 1) if int(i)>0 else '0' for i in x)[::-1]
    return sum([int(y[i])*f(i + 1) for i in range(len(y))])
print([a(n) for n in range(201)]) # Indranil Ghosh, Jun 21 2017

Crossrefs

Cf. A007623, A276008.

Cf. also A257684, A257687, A266123, A266193.

Sequence in context: A037863 A163536 A328828 * A328842 A113302 A292946

Adjacent sequences: A276006 A276007 A276008 * A276010 A276011 A276012

Keyword

nonn,base

Author

Antti Karttunen, Aug 18 2016

Status

approved