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A037860 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*10^i: i=0,1,...,m} is base 10 representation of n.

%I A037860 #11 Jan 21 2018 04:08:24
%S A037860 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,3,2,1,0,0,
%T A037860 0,0,0,0,0,4,3,2,1,0,0,0,0,0,0,5,4,3,2,1,0,0,0,0,0,6,5,4,3,2,1,0,0,0,
%U A037860 0,7,6,5,4,3,2,1,0,0,0,8,7,6,5,4,3,2,1,0,0,9
%N A037860 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*10^i: i=0,1,...,m} is base 10 representation of n.
%C A037860 This is the base-10 down-variation sequence; see A297330.
%H A037860 Clark Kimberling, <a href="/A037860/b037860.txt">Table of n, a(n) for n = 1..10000</a>
%p A037860 A037860 := proc(n)
%p A037860     a := 0 ;
%p A037860     dgs := convert(n,base,10);
%p A037860     for i from 2 to nops(dgs) do
%p A037860         if op(i,dgs)>op(i-1,dgs) then
%p A037860             a := a+op(i,dgs)-op(i-1,dgs) ;
%p A037860         end if;
%p A037860     end do:
%p A037860     a ;
%p A037860 end proc: # _R. J. Mathar_, Oct 19 2015
%t A037860 g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 10; z = 120;
%t A037860 Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037860*)
%t A037860 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037851*)
%Y A037860 Cf. A297330, A037851.
%K A037860 nonn,base
%O A037860 1,20
%A A037860 _Clark Kimberling_
%E A037860 Definition swapped with A037851. - _R. J. Mathar_, Oct 19 2015
%E A037860 Updated by _Clark Kimberling_, Jan 19 2018