%I #15 Aug 11 2014 22:46:11
%S 1,0,3,4,4,0,1,0,2,0,1,1,0,2,10,11,1,0,1,1,0,2,2,0,2,1,2,0,0,3,0,0,2,
%T 0,4,1,0,2,1,0,1,5,2,0,0,6,0,1,0,1,2,0,0,1,0,1,3,2,0,0,1,0,0,3,3,0,1,
%U 1,0,2,1,0,8,1,1,0,0,1,0,2,0,1,2,0,0,3
%N Number of the first odious exponents (A000069) in the prime power factorization of (2n)!.
%C Conjecture: The sequence is unbounded. (This conjecture does not follow from Chen's theorem.)
%H Peter J. C. Moses, <a href="/A240669/b240669.txt">Table of n, a(n) for n = 1..2000</a>
%H Y.-G. Chen, <a href="http://dx.doi.org/10.1016/S0022-314X(03)00013-1">On the parity of exponents in the standard factorization of n!</a>, J. Number Theory, 100 (2003), 326-331.
%e 28! = 2^25*3^13*5^6*7^4*11^2*13^2*17*19*23, and only the first 2 exponents are odious, so a(14) = 2.
%t Map[Count[First[Split[Map[OddQ[DigitCount[#,2][[1]]]&,Last[Transpose[FactorInteger[(2*#)!]]&[#]]]]],True]&,Range[75]] (* _Peter J. C. Moses_, Apr 10 2014 *)
%Y Cf. A000069, A240537, A240606, A240619, A240620, A240668.
%K nonn
%O 1,3
%A _Vladimir Shevelev_, Apr 10 2014