A037818 Number of i such that d(i)>d(i-1), where Sum{d(i)*3^i: i=0,1,....,m} is base 3 representation of n.

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

Offset

1,21

Comments

From Jeffrey Shallit, May 15 2016: (Start)

A "3-regular" sequence that satisfies the recurrences

a(3n+2) = a(n)

a(9n) = a(9n+1) = a(3n)

a(9n+4) = a(3n+1)

a(9n+6) = a(9n+7) = a(n) + 1

a(27n+3) = a(3n) + 1

a(27n+12) = a(9n+3)

a(27n+21) = a(n) + 2

(End)

Links

Table of n, a(n) for n=1..90.

Maple

A037818 := 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+1 ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Oct 15 2015

Mathematica

a[n_] := Count[Differences@ IntegerDigits[n, 3], x_ /; x < 0]; Array[a, 90] (* Giovanni Resta, May 15 2016 *)

Crossrefs

Cf. A007089, A037801.

Sequence in context: A178535 A025449 A047988 * A087116 A033264 A258045

Adjacent sequences: A037815 A037816 A037817 * A037819 A037820 A037821

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Sign in name corrected by R. J. Mathar, Oct 15 2015

Status

approved