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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
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<p else a007623(n//p, p+1)*10 + n%p
def a(n):
x=str(a007623(n))[::-1]
y="".join(str(i) if i + 1==int(x[i]) else x[i] for i in range(len(x)))[1:]
return 0 if n==0 else sum(int(y[i])*f(i + 1) for i in range(len(y)))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 24 2017
CROSSREFS
Left inverse of A153880.
Sequence in context: A331854 A093875 A329242 * A114214 A321318 A270362
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Dec 23 2015
STATUS
approved

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Last modified May 20 05:07 EDT 2024. Contains 372703 sequences. (Running on oeis4.)