%I A135650
%S A135650 110,11100,111110000,1111111000000,1111111111111000000000000,
%T A135650 111111111111111110000000000000000,
%U A135650 1111111111111111111000000000000000000
%N A135650 Even perfect numbers written in base 2.
%C A135650 The number of digits of a(n) is equal to 2*A000043(n)-1. The central 
               digit is "1". The first digits are "1". The last digits are "0". 
               The number of digits "1" is equal A000043(n). The number of digits 
               "0" is equal A000043(n)-1.
%C A135650 The concatenation of digits "1" of a(n) gives the n-th Mersenne prime 
               written in binary (see A117293(n)).
%C A135650 Also, the number of digits of a(n) is equal to A133033(n), the number 
               of proper divisors of n-th even perfect number.
%H A135650 O. E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica 
               de los numeros primos y perfectos</a>.
%e A135650 a(3)=111110000 because the 3rd. even perfect number is 496 and 496 written 
               in base 2 is 111110000. Note that 11111 is the 3rd. Mersenne prime 
               A000668(3)=31 written in base 2.
%Y A135650 Cf. A000043, A000396, A000668, A090748, A117293.
%Y A135650 Cf. A061645, A133033.
%Y A135650 Sequence in context: A058935 A109241 A090490 this_sequence A097580 A139478 
               A143750
%Y A135650 Adjacent sequences: A135647 A135648 A135649 this_sequence A135651 A135652 
               A135653
%K A135650 base,nonn
%O A135650 1,1
%A A135650 Omar E. Pol (info(AT)polprimos.com), Feb 21 2008, Feb 22 2008, Apr 28 
               2009