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 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. 13
 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 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

0 else '0' for i in x])[::-1] return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in range(len(y))]) def a(n): return 0 if n==0 else n%2 + a(a257684(n)) print [a(n) for n in range(101)] # Indranil Ghosh, Jun 20 2017 CROSSREFS Cf. A000035, A007623, A257684. Cf. also A257511. Sequence in context: A141747 A239706 A328616 * A293896 A066416 A292342 Adjacent sequences:  A260733 A260734 A260735 * A260737 A260738 A260739 KEYWORD nonn,base AUTHOR Antti Karttunen, Aug 27 2015 STATUS approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)