A037854 Sum_{i=1..m, d(i)>d(i-1)} d(i)-d(i-1), where Sum_{i=0..m} d(i)*4^i is the base 4 representation of n.

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

This is the base-4 down-variation sequence; see A297330. - Clark Kimberling, Jan 18 2018

Links

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

Crossrefs

Cf. A297330.

Programs

Maple

A037854 := proc(n)
    a := 0 ;
    dgs := convert(n,base,4);
    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

d[n_] := d[n] = Differences[RealDigits[n, 4][[1]]]
Table[Total[Select[d[n], # > 0 &]], {n, 1, z}];  (* A037845 *)
-Table[Total[Select[d[n], # < 0 &]], {n, 1, z}]; (* A037854 *)
(* Clark Kimberling, Oct 20 2015 *)

Extensions

Definition swapped with A037845 by R. J. Mathar, Oct 19 2015