A037850 - OEIS

%I #11 Jan 20 2018 11:11:53

%S 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 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 0,0,1,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,0

%N 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 This is the base-9 up-variation sequence; see A297330. - _Clark Kimberling_, Jan 18 2017

%H Clark Kimberling, <a href="/A037850/b037850.txt">Table of n, a(n) for n = 1..10000</a>

%p A037850 := proc(n)

%p     a := 0 ;

%p     dgs := convert(n,base,9);

%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 = 9; z = 120;

%t Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037859*)

%t Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037850*)

%Y Cf. A297330, A037859.

%K nonn,base

%O 1,12

%A _Clark Kimberling_

%E Definition swapped with A037859. - _R. J. Mathar_, Oct 19 2015

%E Updated by _Clark Kimberling_, Jan 19 2018