A043278 Maximal run length in base 4 representation of n.

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Sequences A031942 (or A043090), A037977, A037978, A037979 list numbers for which a(n)=1, a(n)=2, a(n)=3, a(n)=4. - M. F. Hasler, Jul 23 2013

Links

• Winston de Greef, Table of n, a(n) for n = 1..10000

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:
A043278 := proc(n)
    convert(n,base,4) ;
    mRunLen(%) ;
end proc: # R. J. Mathar, Jul 26 2015

Mathematica

Table[Max[Length/@Split[IntegerDigits[n,4]]],{n,100}] (* Harvey P. Dale, Jan 21 2014 *)

PARI

A043278(n, b=4)={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