A037859 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*9^i: i=0,1,...,m} is base 9 representation of n.

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

This is the base-9 down-variation sequence; see A297330. - Clark Kimberling, Jan 18 2017

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A297330, A037850.

Programs

Maple

A037859 := proc(n)
    a := 0 ;
    dgs := convert(n,base,9);
    for i from 2 to nops(dgs) do
        if op(i,dgs)>op(i-1,dgs) then
            a := a+op(i,dgs)-op(i-1,dgs) ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Oct 19 2015

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 9; z = 120;
Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037859*)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037850*)

Extensions

Definition swapped with A037850. - R. J. Mathar, Oct 19 2015

Updated by Clark Kimberling, Jan 19 2018