This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
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.
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 *)
from sympy import factorial as f def a007623(n, p=2): return n if n0 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
(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)))))))
n A007623(n) [subtract 1 from digits > 1 a(n)
[in factorial then shift one digit right] [reinterpret
base] in decimal]
0 0 -> 0 = 0
1 1 -> 0 = 0
2 10 -> 1 = 1
3 11 -> 1 = 1
4 20 -> 1 = 1
5 21 -> 1 = 1
6 100 -> 10 = 2
7 101 -> 10 = 2
8 110 -> 11 = 3
9 111 -> 11 = 3
10 120 -> 11 = 3
11 121 -> 11 = 3
12 200 -> 10 = 2
13 201 -> 10 = 2
14 210 -> 11 = 3
15 211 -> 11 = 3
16 220 -> 11 = 3
17 221 -> 11 = 3
18 300 -> 20 = 4