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 A266193 Decrement by 1 all maximal digits in factorial base representation of n and then shift it one digit right. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 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. LINKS Antti Karttunen, Table of n, a(n) for n = 0..10080 FORMULA Other identities. For all n >= 0: a(A153880(n)) = n. EXAMPLE 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 PROG (MIT/GNU Scheme) (define (A266193 n) (let loop ((n n) (z 0) (i 2) (f 0)) (cond ((zero? n) z) (else (let ((d (remainder n i))) (loop (quotient n i) (+ z (* f (- d (if (< d (- i 1)) 0 1)))) (+ 1 i) (if (zero? f) 1 (* f (- i 1))))))))) (Python) from sympy import factorial as f def a007623(n, p=2): return n if n

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)