A196272 - OEIS

%I #22 Feb 15 2020 23:58:21

%S 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,

%T 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,

%U 0,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,3

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

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

%C 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

%H T. D. Noe, <a href="/A196272/b196272.txt">Table of n, a(n) for n = 0..1000</a>

%e 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".

%p A196272 := proc(n)

%p         local a, dgs ;

%p         a := 0 ;

%p         dgs := convert(n, base, 4) ;

%p         for i from 1 to nops(dgs)-1 do

%p                 if op(i, dgs)=1 and op(i+1, dgs)=1 then

%p                         a := a+1 ;

%p                 end if;

%p         end do;

%p         a ;

%p end proc:

%p seq(A196272(n), n=0..100) ; # _R. J. Mathar_, Sep 30 2011

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

%Y Cf. A007090, A014081, A196096.

%K nonn,easy,base

%O 0,22

%A _Jonathan Vos Post_, Sep 29 2011