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A037859 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*9^i: i=0,1,...,m} is base 9 representation of n.

%I A037859 #11 Jan 21 2018 04:08:17
%S A037859 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,3,2,1,0,0,0,0,0,
%T A037859 0,4,3,2,1,0,0,0,0,0,5,4,3,2,1,0,0,0,0,6,5,4,3,2,1,0,0,0,7,6,5,4,3,2,
%U A037859 1,0,0,8,7,6,5,4,3,2,1,0,1,1,1,1,1,1,1,1,1,1
%N A037859 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*9^i: i=0,1,...,m} is base 9 representation of n.
%C A037859 This is the base-9 down-variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017
%H A037859 Clark Kimberling, <a href="/A037859/b037859.txt">Table of n, a(n) for n = 1..10000</a>
%p A037859 A037859 := proc(n)
%p A037859     a := 0 ;
%p A037859     dgs := convert(n,base,9);
%p A037859     for i from 2 to nops(dgs) do
%p A037859         if op(i,dgs)>op(i-1,dgs) then
%p A037859             a := a+op(i,dgs)-op(i-1,dgs) ;
%p A037859         end if;
%p A037859     end do:
%p A037859     a ;
%p A037859 end proc: # _R. J. Mathar_, Oct 19 2015
%t A037859 g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 9; z = 120;
%t A037859 Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037859*)
%t A037859 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037850*)
%Y A037859 Cf. A297330, A037850.
%K A037859 nonn,base
%O A037859 1,18
%A A037859 _Clark Kimberling_
%E A037859 Definition swapped with A037850. - _R. J. Mathar_, Oct 19 2015
%E A037859 Updated by _Clark Kimberling_, Jan 19 2018