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

1,8

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

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 *)

Crossrefs

Cf. A297330.

Sequence in context: A362427 A218253 A037872 * A362633 A091229 A290255

Adjacent sequences: A037851 A037852 A037853 * A037855 A037856 A037857

Keyword

nonn,base

Author

Clark Kimberling

Extensions

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

Status

approved