

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) = n1. [n!1 gives also the first position where n1 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 onebased 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 memoizationmacro 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



