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)

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

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 * A337976 A125005 A309367

Adjacent sequences: A275944 A275945 A275946 * A275948 A275949 A275950

Keyword

nonn,base

Author

Antti Karttunen, Aug 15 2016

Status

approved