A275946 Number of nonzero digits that are the sole occupants of their slope in factorial base representation: a(n) = A056169(A275734(n)). (See comments for more exact definition.)

0, 1, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 1, 2, 0, 1, 2, 1, 1, 0, 2, 1, 0, 0, 1, 2, 2, 3, 2, 1, 2, 3, 3, 4, 3, 2, 2, 3, 1, 2, 3, 2, 2, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 1, 0, 1, 1, 2, 1, 0, 2, 3, 1, 2, 3, 2, 2, 1, 3, 2, 1, 1, 1, 2, 0, 1, 2, 1, 2, 3, 1, 2, 3, 2, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 2, 1, 3, 2, 1, 1, 2, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1

Offset: 0

Author

Antti Karttunen, Aug 15 2016

Keywords

• nonn
• base

Comments

Total number of such nonzero digits d_x in the factorial base representation (A007623) of n for which it holds that for all other nonzero digits d_y present (i_x - d_x) <> (i_y - d_y), where i_x and i_y are the indices of the digits d_x and d_y respectively.

Equally: Number of digit slopes occupied by just one nonzero digit in the factorial base representation of n. In other words, a(n) is the number of elements with multiplicity one in multiset [(i_x - d_x) | where d_x ranges over each nonzero digit present and i_x is its position from the right].

Examples

			For n=2, in factorial base "10", there is only one slope occupied by a single nonzero digit (1 is on the sub-maximal slope as 2-1 = 1), thus a(2) = 1.
For n=3, in factorial base "11", there are two occupied slopes, each having just one digit present, thus a(3) = 2.
For n=5, in factorial base "21", there is just one distinct occupied slope, but it contains two nonzero digits (2 and 1 both occupy the maximal slope as 2-2 = 1-1 = 0), thus there are no slopes with just one nonzero digit and a(5) = 0.
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 only one of the slopes is occupied by a lonely occupant and a(525) = 1.
		

Links

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

Crossrefs

Cf. A056169, A275734.

Cf. also A060502, A060130, A225901, A275947, A275948, A275962.

Programs

Scheme

(define (A275946 n) (A056169 (A275734 n)))

Formula

a(n) = A056169(A275734(n)).

Other identities. For all n >= 0.

a(n) = A275948(A225901(n)).

A060502(n) = a(n) + A275947(n).

A060130(n) = a(n) + A275962(n).