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A037857 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*7^i: i=0,1,...,m} is base 7 representation of n.

%I A037857 #13 Nov 22 2021 10:01:49
%S A037857 0,0,0,0,0,0,1,0,0,0,0,0,0,2,1,0,0,0,0,0,3,2,1,0,0,0,0,4,3,2,1,0,0,0,
%T A037857 5,4,3,2,1,0,0,6,5,4,3,2,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,2,1,0,0,0,0,
%U A037857 0,3,2,1,0,0,0,0,4,3,2,1,0,0,0,5,4,3,2,1,0,0
%N A037857 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*7^i: i=0,1,...,m} is base 7 representation of n.
%C A037857 This is the base-7 down-variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017
%H A037857 Clark Kimberling, <a href="/A037857/b037857.txt">Table of n, a(n) for n = 1..10000</a>
%p A037857 A037857 := proc(n)
%p A037857     a := 0 ;
%p A037857     dgs := convert(n,base,7);
%p A037857     for i from 2 to nops(dgs) do
%p A037857         if op(i,dgs)>op(i-1,dgs) then
%p A037857             a := a+op(i,dgs)-op(i-1,dgs) ;
%p A037857         end if;
%p A037857     end do:
%p A037857     a ;
%p A037857 end proc: # _R. J. Mathar_, Oct 19 2015
%t A037857 g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 7; z = 120;
%t A037857 Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037857*)
%t A037857 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037848*)
%K A037857 nonn,base
%O A037857 1,14
%A A037857 _Clark Kimberling_
%E A037857 Definition swapped with A037848. - _R. J. Mathar_, Oct 19 2015
%E A037857 Updated by _Clark Kimberling_, Jan 19 2018