

A275962


Total number of nonzero digits that occur on the multiply occupied slopes of the factorial base representation of n: a(n) = A275812(A275734(n)). (See comments for more exact definition).


9



0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 3, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 4, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 3, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 3, 3, 2, 4, 0, 2, 2, 4, 2, 3, 0, 2, 0, 2, 2, 3, 0, 2, 0, 2, 2, 3, 0, 2, 2, 4, 2, 3, 2, 3, 2, 3, 3, 4, 0
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OFFSET

0,6


COMMENTS

a(n) gives the total number of elements (counted with multiplicity) 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) = A275812(A275734(n)).
Other identities and observations. For all n >= 0.
a(n) = A275964(A225901(n)).
a(n) = A060130(n)  A275946(n).
a(n) >= A275947(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 the digits "4..1.", and the subsubsubmaximal just "1..." (the 1 in the position 4 from right is the sole occupier of its own slope). There are two slopes with more than one nonzero digit, each having two such digits, and thus a(525) = 2+2 = 4.
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 elements that occur multiple times are [0, 0, 1, 1], thus a(525) = 4.


PROG

(Scheme) (define (A275962 n) (A275812 (A275734 n)))


CROSSREFS

Cf. A275734, A275812.
Cf. A275804 (indices of zeros), A275805 (of nonzeros).
Cf. also A060130, A225901, A275946, A275947, A275964.
Sequence in context: A126825 A045833 A117896 * A132976 A143840 A028649
Adjacent sequences: A275959 A275960 A275961 * A275963 A275964 A275965


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Aug 15 2016


STATUS

approved



