A037853 Sum{d(i)-d(i-1): d(i)>d(i-1), i=1,...,m}, where Sum{d(i)*3^i: i=0,1,...,m} is base 3 representation of n.

0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 0, 2, 1, 0, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 0, 0, 2, 1, 0, 2, 2, 2, 2, 1, 1, 2, 1, 0, 2, 2, 2, 3, 2, 2, 4, 3, 2, 2, 2, 2, 2, 1, 1, 3, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 1, 1, 2, 1, 1, 3, 2, 1, 2

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

This is the base-3 down-variation sequence; see A297330. - Clark Kimberling, Jan 18 2018

Links

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

Crossrefs

Cf. A037844, A297330.

Programs

Maple

A037853 := proc(n)
    a := 0 ;
    dgs := convert(n,base,3);
    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 16 2015

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]]; b = 3; z = 120;
Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (*A037853*)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}];   (*A037844*)
(* Clark Kimberling, Jan 18 2018 *)

Extensions

Definition corrected by R. J. Mathar, Oct 16 2015