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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 (list; graph; refs; listen; history; text; internal format)
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 sub-maximal digits "4..1.", and the sub-sub-sub-maximal 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 (digit-position - digit-value) 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 * A125005 A122179 A125203

Adjacent sequences:  A275944 A275945 A275946 * A275948 A275949 A275950

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Aug 15 2016

STATUS

approved

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Last modified February 25 08:12 EST 2018. Contains 299646 sequences. (Running on oeis4.)