A219651 a(n) = n minus (sum of digits in factorial base expansion of n).

0, 0, 1, 1, 2, 2, 5, 5, 6, 6, 7, 7, 10, 10, 11, 11, 12, 12, 15, 15, 16, 16, 17, 17, 23, 23, 24, 24, 25, 25, 28, 28, 29, 29, 30, 30, 33, 33, 34, 34, 35, 35, 38, 38, 39, 39, 40, 40, 46, 46, 47, 47, 48, 48, 51, 51, 52, 52, 53, 53, 56, 56, 57, 57, 58, 58, 61, 61

Offset: 0

Author

Antti Karttunen, Nov 25 2012

Keywords

• nonn
• base

Comments

See A007623 for the factorial base number system representation.

Links

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

Crossrefs

Bisection: A219650. Analogous sequence for binary system: A011371, for Zeckendorf expansion: A219641.

Cf. A007623, A034968, A219652-A219655, A219656, A219659, A219666.

Programs

Mathematica

(* First run program for A007623 to define factBaseIntDs *) Table[n - Plus@@factBaseIntDs[n], {n, 0, 99}] (* Alonso del Arte, Nov 25 2012 *)

Python

from itertools import count
def A219651(n):
    c, f = 0, 1
    for i in count(2):
        f *= i
        if f>n:
            break
        c += (i-1)*(n//f)
    return c # Chai Wah Wu, Oct 11 2024

Scheme

(define (A219651 n) (- n (A034968 n)))

Formula

a(n) = n - A034968(n).