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A037858 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*8^i: i=0,1,...,m} is base 8 representation of n.

%I A037858 #11 Jan 19 2018 19:36:30
%S A037858 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,3,2,1,0,0,0,0,0,4,3,2,
%T A037858 1,0,0,0,0,5,4,3,2,1,0,0,0,6,5,4,3,2,1,0,0,7,6,5,4,3,2,1,0,1,1,1,1,1,
%U A037858 1,1,1,1,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,3,2,1
%N A037858 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*8^i: i=0,1,...,m} is base 8 representation of n.
%C A037858 This is the base-8 down-variation sequence; see A297330.
%H A037858 Clark Kimberling, <a href="/A037858/b037858.txt">Table of n, a(n) for n = 1..10000</a>
%p A037858 A037858 := proc(n)
%p A037858     a := 0 ;
%p A037858     dgs := convert(n,base,8);
%p A037858     for i from 2 to nops(dgs) do
%p A037858         if op(i,dgs)>op(i-1,dgs) then
%p A037858             a := a+op(i,dgs)-op(i-1,dgs) ;
%p A037858         end if;
%p A037858     end do:
%p A037858     a ;
%p A037858 end proc: # _R. J. Mathar_, Oct 19 2015
%t A037858 g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 8; z = 120;
%t A037858 Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037858*)
%t A037858 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037849*)
%Y A037858 Cf. A297330.
%K A037858 nonn,base
%O A037858 1,16
%A A037858 _Clark Kimberling_
%E A037858 Definition swapped with A037849. - _R. J. Mathar_, Oct 19 2015
%E A037858 Updated by _Clark Kimberling_, Jan 19 2018