%I #13 Nov 22 2021 10:01:49

%S 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 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 0,3,2,1,0,0,0,0,4,3,2,1,0,0,0,5,4,3,2,1,0,0

%N 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 This is the base-7 down-variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017

%H Clark Kimberling, <a href="/A037857/b037857.txt">Table of n, a(n) for n = 1..10000</a>

%p A037857 := proc(n)

%p a := 0 ;

%p dgs := convert(n,base,7);

%p for i from 2 to nops(dgs) do

%p if op(i,dgs)>op(i-1,dgs) then

%p a := a+op(i,dgs)-op(i-1,dgs) ;

%p end if;

%p end do:

%p a ;

%p end proc: # _R. J. Mathar_, Oct 19 2015

%t g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 7; z = 120;

%t Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}]; (*A037857*)

%t Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (*A037848*)

%K nonn,base

%O 1,14

%A _Clark Kimberling_

%E Definition swapped with A037848. - _R. J. Mathar_, Oct 19 2015

%E Updated by _Clark Kimberling_, Jan 19 2018