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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A280605 A218253 A037872 * A091229 A290255 A283982

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

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Last modified October 19 01:20 EDT 2019. Contains 328211 sequences. (Running on oeis4.)