A196272 Number of occurrences of '11' in base-4 expansion of n.

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

Offset: 0

Author

Jonathan Vos Post, Sep 29 2011

Keywords

• nonn
• easy
• base

Comments

This is to base 4 A007090 as A196096 is to base 3 and A007089 as A014081 is to base 2 A007088.

Records occur at places where n = '111...11' in base b, that is n = (b^(k+1)-1)/(b-1) for some k > 0, in particular for b=4 as listed in A002450(k+1). - R. J. Mathar, Sep 30 2011

Examples

			a(21) = 2 because 21 (base 10) = 111 (base 4), whose first two digits are 1's, and whose rightmost two digits are the second substring of "11".
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007090, A014081, A196096.

Programs

Maple

A196272 := proc(n)
        local a, dgs ;
        a := 0 ;
        dgs := convert(n, base, 4) ;
        for i from 1 to nops(dgs)-1 do
                if op(i, dgs)=1 and op(i+1, dgs)=1 then
                        a := a+1 ;
                end if;
        end do;
        a ;
end proc:
seq(A196272(n), n=0..100) ; # R. J. Mathar, Sep 30 2011

Mathematica

Table[d = IntegerDigits[n, 4]; Count[Partition[d, 2, 1], {1, 1}], {n, 0, 100}] (* T. D. Noe, Sep 30 2011 *)