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A037850 a(n)=Sum{d(i-1)-d(i): d(i) where Sum{d(i)*9^i: i=0,1,...,m} is the base 9 representation of n.

%I A037850 #11 Jan 20 2018 11:11:53
%S A037850 0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,0,0,0,1,2,3,4,5,6,0,0,0,0,1,2,3,4,
%T A037850 5,0,0,0,0,0,1,2,3,4,0,0,0,0,0,0,1,2,3,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,
%U A037850 0,0,1,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,0
%N A037850 a(n)=Sum{d(i-1)-d(i): d(i)<d(i-1), i=1,...,m}, where Sum{d(i)*9^i: i=0,1,...,m} is the base 9 representation of n.
%C A037850 This is the base-9 up-variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017
%H A037850 Clark Kimberling, <a href="/A037850/b037850.txt">Table of n, a(n) for n = 1..10000</a>
%p A037850 A037850 := proc(n)
%p A037850     a := 0 ;
%p A037850     dgs := convert(n,base,9);
%p A037850     for i from 2 to nops(dgs) do
%p A037850         if op(i,dgs)<op(i-1,dgs) then
%p A037850             a := a-op(i,dgs)+op(i-1,dgs) ;
%p A037850         end if;
%p A037850     end do:
%p A037850     a ;
%p A037850 end proc: # _R. J. Mathar_, Oct 19 2015
%t A037850 g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 9; z = 120;
%t A037850 Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037859*)
%t A037850 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037850*)
%Y A037850 Cf. A297330, A037859.
%K A037850 nonn,base
%O A037850 1,12
%A A037850 _Clark Kimberling_
%E A037850 Definition swapped with A037859. - _R. J. Mathar_, Oct 19 2015
%E A037850 Updated by _Clark Kimberling_, Jan 19 2018