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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

%I #21 Jun 19 2017 13:52:47

%S 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,

%T 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,

%U 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

%N 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).

%C 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].

%H Antti Karttunen, <a href="/A275962/b275962.txt">Table of n, a(n) for n = 0..40320</a>

%H Indranil Ghosh, <a href="/A275962/a275962.txt">Python program for computing this sequence</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%F a(n) = A275812(A275734(n)).

%F Other identities and observations. For all n >= 0.

%F a(n) = A275964(A225901(n)).

%F a(n) = A060130(n) - A275946(n).

%F a(n) >= A275947(n).

%e 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.

%e 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.

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

%Y Cf. A275734, A275812.

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

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

%K nonn,base

%O 0,6

%A _Antti Karttunen_, Aug 15 2016

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