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%I #5 Mar 11 2014 01:34:11
%S 101,11011,111101111,1111110111111,1111111111110111111111111,
%T 111111111111111101111111111111111,
%U 1111111111111111110111111111111111111
%N n-th perfect number minus 1, written in base 2.
%C Subset of A138148, cyclops numbers with binary digits, only.
%C Subset of A002113, palindromes in base 10.
%C a(n) has 2*A090748(n) digits 1.
%C The number of digits of a(n) is 2*A000043(n)-1, equal to A133033(n), the number of proper divisors of n-th perfect number.
%C a(n) = (A135627(n) written in base 2).
%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%F a(n) = A138148(A090748(n)).
%e n ... A000396(n) - 1 = A135627(n) ............. a(n)
%e 1 ............ 6 - 1 = ...... 5 ............... 101
%e 2 ........... 28 - 1 = ..... 27 .............. 11011
%e 3 .......... 496 - 1 = .... 495 ............ 111101111
%e 4 ......... 8128 - 1 = ... 8127 .......... 1111110111111
%e 5 ..... 33550336 - 1 = 33550335 .... 1111111111110111111111111
%Y Cf. A000043, A000396, A090748, A133033, A134808, A135627, A138131, A138148.
%K nonn,base,less
%O 1,1
%A _Omar E. Pol_, Apr 08 2008, Apr 09 2008, Apr 14 2008