A266123 Decrement by 1 all digits > 1 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, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18

Offset

0,7

Links

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

Index entries for sequences related to factorial base representation

Example

   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

Prog

(MIT/GNU Scheme)
(define (A266123 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 1) 0 1)))) (+ 1 i) (if (zero? f) 1 (* f (- i 1)))))))))

Crossrefs

Cf. A007623, A257684, A266193.

Sequence in context: A321859 A321860 A348459 * A115230 A363937 A338686

Adjacent sequences: A266120 A266121 A266122 * A266124 A266125 A266126

Keyword

nonn,base

Author

Antti Karttunen, Dec 23 2015

Status

approved