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

0,22

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

Links

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

Example

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".

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 *)

Crossrefs

Cf. A007090, A014081, A196096.

Sequence in context: A108511 A261160 A270668 * A086073 A053622 A016408

Adjacent sequences: A196269 A196270 A196271 * A196273 A196274 A196275

Keyword

nonn,easy,base

Author

Jonathan Vos Post, Sep 29 2011

Status

approved