A266193 Decrement by 1 all maximal digits in factorial base representation of n and then shift it one digit right.

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

Offset: 0

Author

Antti Karttunen, Dec 23 2015

Keywords

• nonn
• base

Comments

By "maximal digits" are here understood any digit k that occurs in position k, digit-positions numbered from the right and starting from 1. For example in A007623(677) = "53021", the digits "5" and "1" are maximal, because no larger digits will fit into those positions in a well-formed factorial base representation of a natural number.

Examples

			    n     A007623(n)  [subtract 1 from max.digits      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     ->     20                         =  4
   13       201     ->     20                         =  4
   14       210     ->     21                         =  5
   15       211     ->     21                         =  5
   16       220     ->     21                         =  5
   17       221     ->     21                         =  5
   18       300     ->     20                         =  4
  ...
   23       321     ->     21                         =  5
  119      4321     ->    321                         = 23
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A007623, A257684, A266123.

Left inverse of A153880.

Programs

Python

from sympy import factorial as f
def a007623(n, p=2): return n if n
Indranil Ghosh, Jun 24 2017

Formula

Other identities. For all n >= 0:

a(A153880(n)) = n.