A037858 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*8^i: i=0,1,...,m} is base 8 representation of n.

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

Offset

1,16

Comments

This is the base-8 down-variation sequence; see A297330.

Links

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

Maple

A037858 := proc(n)
    a := 0 ;
    dgs := convert(n, base, 8);
    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 = 8; z = 120;
Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037858*)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037849*)

Crossrefs

Cf. A297330.

Sequence in context: A298826 A374246 A074079 * A037876 A263774 A161519

Adjacent sequences: A037855 A037856 A037857 * A037859 A037860 A037861

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Definition swapped with A037849. - R. J. Mathar, Oct 19 2015

Updated by Clark Kimberling, Jan 19 2018

Status

approved