A043277 Maximal run length in base 3 representation of n.

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Sequences A031941, A037973, A037974, A037975 list numbers for which a(n)=1, a(n)=2, a(n)=3, a(n)=4. - M. F. Hasler, Jul 23 2013

A003462 gives the positions of records. - R. J. Mathar, Jul 26 2015

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A043276-A043290 for base-2 to base-16 analogs.

Programs

Maple

mRunLen := proc(L)
    if nops(L) = 0 then
        0;
    else
        a := 1 ;
        for i from 2 to nops(L) do
            if op(i,L) = op(i-1,L) then
                a := a+1 ;
            else
                a := max(a, procname([op(i..nops(L),L)])) ;
                break;
            end if;
        end do:
        a ;
    end if ;
end proc:
A043277 := proc(n)
    convert(n,base,3) ;
    mRunLen(%) ;
end proc:
seq(A043277(n),n=1..100) ; # R. J. Mathar, Jul 26 2015

Mathematica

Table[Max[Length/@Split[IntegerDigits[n,3]]],{n,90}] (* Harvey P. Dale, Aug 24 2019 *)

PARI

A043277(n, b=3)={my(m,c=1); while(n>0, n%b==(n\=b)%b && c++ && next; m=max(m, c); c=1); m} \\ - M. F. Hasler, Jul 23 2013