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).

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

Offset: 0

Author

Antti Karttunen, Aug 15 2016

Keywords

• nonn
• base

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].

Examples

			For n=525, in factorial base "41311", there are three occupied slopes. The maximal slope contains the nonzero digits "3.1", the sub-maximal the 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). 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 (digit-position - digit-value) 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.
		

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

Crossrefs

Cf. A275734, A275812.

Cf. A275804 (indices of zeros), A275805 (of nonzeros).

Cf. also A060130, A225901, A275946, A275947, A275964.

Programs

Scheme

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

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).