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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).

%I A275947 #22 Jun 02 2025 12:19:32
%S A275947 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,
%T A275947 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,
%U A275947 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
%N 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).
%C A275947 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].
%H A275947 Antti Karttunen, <a href="/A275947/b275947.txt">Table of n, a(n) for n = 0..40320</a>
%H A275947 Indranil Ghosh, <a href="/A275947/a275947.txt">Python program for computing this sequence</a>
%H A275947 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A275947 a(n) = A056170(A275734(n)).
%F A275947 Other identities and observations. For all n >= 0.
%F A275947 a(n) = A275949(A225901(n)).
%F A275947 A060502(n) = A275946(n) + a(n).
%F A275947 a(n) <= A275962(n).
%e A275947 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.
%e A275947 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.
%o A275947 (Scheme) (define (A275947 n) (A056170 (A275734 n)))
%Y A275947 Cf. A056170, A275734.
%Y A275947 Cf. A275804 (indices of zeros), A275805 (of nonzeros).
%Y A275947 Cf. also A060502, A225901, A275946, A275949, A275962.
%K A275947 nonn,base
%O A275947 0,60
%A A275947 _Antti Karttunen_, Aug 15 2016