A037845 a(n) = Sum_{i=1..m, d(i)<d(i-1)} d(i-1)-d(i), where Sum_{i=0..m} d(i)*4^i is the base 4 representation of n.

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

Offset

1,7

Links

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

Maple

A037845 := 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

Sequence in context: A089813 A343023 A337760 * A037881 A024326 A287619

Adjacent sequences: A037842 A037843 A037844 * A037846 A037847 A037848

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Definition swapped with A037854. - R. J. Mathar, Oct 19 2015

Status

approved