

A275947


Number of distinct slopes with multiple nonzero digits in factorial base representation of n: a(n) = A056170(A275734(n)). (See comments for more exact definition)


9



0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0
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OFFSET

0,60


COMMENTS

a(n) gives the number of distinct elements that have multiplicity > 1 in a multiset [(i_x  d_x)  where d_x ranges over each nonzero digit present and i_x is its position from the right].


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..40320
Indranil Ghosh, Python program for computing this sequence
Index entries for sequences related to factorial base representation


FORMULA

a(n) = A056170(A275734(n)).
Other identities and observations. For all n >= 0.
a(n) = A275949(A225901(n)).
A060502(n) = A275946(n) + a(n).
a(n) <= A275962(n).


EXAMPLE

For n=525, in factorial base "41311", there are three occupied slopes. The maximal slope contains the nonzero digits "3.1", the submaximal digits "4..1.", and the subsubsubmaximal just "1..." (the 1 in the position 4 from right is the sole occupier of its own slope). Thus there are two slopes with more than one nonzero digit, and a(525) = 2.
Equally, when we form a multiset of (digitposition  digitvalue) differences for all nonzero digits present in "41311", we obtain a multiset [0, 0, 1, 1, 3], in which the distinct elements that occur multiple times are 0 and 1, thus a(525) = 2.


PROG

(Scheme) (define (A275947 n) (A056170 (A275734 n)))


CROSSREFS

Cf. A056170, A275734.
Cf. A275804 (indices of zeros), A275805 (of nonzeros).
Cf. also A060502, A225901, A275946, A275949, A275962.
Sequence in context: A285716 A101606 A257469 * A337976 A125005 A309367
Adjacent sequences: A275944 A275945 A275946 * A275948 A275949 A275950


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Aug 15 2016


STATUS

approved



