A037850 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.

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

Offset

1,12

Comments

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

Links

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

Maple

A037850 := 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*)

Crossrefs

Cf. A297330, A037859.

Sequence in context: A087412 A024684 A265538 * A037886 A031045 A010877

Adjacent sequences: A037847 A037848 A037849 * A037851 A037852 A037853

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Definition swapped with A037859. - R. J. Mathar, Oct 19 2015

Updated by Clark Kimberling, Jan 19 2018

Status

approved