login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A260736 a(0) = 0; for n >= 1, a(n) = A000035(n) + a(A257684(n)); in the factorial representation of n the number of digits with maximal possible value allowed in its location. 12
0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 3, 4, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

In the factorial representation of n, given as {d_k, ..., d_3, d_2, d_1}, the maximal allowed digit for any position j is j. This sequence gives how many digits in the whole representation [A007623(n)] attain that maximum allowed value.

LINKS

Table of n, a(n) for n=0..120.

Index entries for sequences related to factorial base representation

FORMULA

a(0) = 0; for n >= 1, a(n) = A000035(n) + a(A257684(n)).

Other identities. For all n >= 1:

a(n!-1) = n-1. [n!-1 gives also the first position where n-1 occurs.]

EXAMPLE

For n=19, which has factorial representation "301", the digits at position 1 and 3, namely "1" and "3" are equal to their one-based position index, in other words, the maximal digits allowed in those positions (while "0" at position 2 is not), thus a(19) = 2.

PROG

(Scheme, with memoization-macro definec)

(definec (A260736 n) (if (zero? n) 0 (+ (A000035 n) (A260736 (A257684 n)))))

(Python)

from sympy import factorial as f

def a007623(n, p=2): return n if n<p else a007623(int(n/p), p+1)*10 + n%p

def a257684(n):

    x=str(a007623(n))[:-1]

    y="".join([str(int(i) - 1) if int(i)>0 else '0' for i in x])[::-1]

    return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in xrange(len(y))])

def a(n): return 0 if n==0 else n%2 + a(a257684(n))

print [a(n) for n in xrange(101)] # Indranil Ghosh, Jun 20 2017

CROSSREFS

Cf. A000035, A007623, A257684.

Cf. also A257511.

Sequence in context: A321396 A141747 A239706 * A293896 A066416 A292342

Adjacent sequences:  A260733 A260734 A260735 * A260737 A260738 A260739

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Aug 27 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 09:24 EST 2018. Contains 317348 sequences. (Running on oeis4.)