|
%I #20 Jun 19 2017 18:44:59
%S 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 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 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 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 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 Antti Karttunen, <a href="/A275947/b275947.txt">Table of n, a(n) for n = 0..40320</a>
%H Indranil Ghosh, <a href="/A275947/a275947.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) = A056170(A275734(n)).
%F Other identities and observations. For all n >= 0.
%F a(n) = A275949(A225901(n)).
%F A060502(n) = A275946(n) + a(n).
%F a(n) <= A275962(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 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 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 (Scheme) (define (A275947 n) (A056170 (A275734 n)))
%Y Cf. A056170, A275734.
%Y Cf. A275804 (indices of zeros), A275805 (of nonzeros).
%Y Cf. also A060502, A225901, A275946, A275949, A275962.
%K nonn,base
%O 0,60
%A _Antti Karttunen_, Aug 15 2016
|
