This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A240672 #12 Aug 11 2014 22:46:11 %S A240672 0,1,0,0,0,2,0,3,0,1,0,0,4,0,0,0,0,2,0,0,1,0,0,1,0,0,0,1,2,0,1,2,0,1, %T A240672 0,0,2,0,0,2,0,0,0,1,1,0,2,0,2,0,0,1,1,0,2,0,0,0,9,2,0,1,1,0,0,2,0,0, %U A240672 1,0,0,1,0,0,0,2,1,0,2,0,3,0,0,1,1,0,2 %N A240672 Number of the first evil exponents (A001969) in the prime power factorization of (2n)!. %C A240672 Conjecture: The sequence is unbounded. (This conjecture does not follow from Chen's theorem.) %H A240672 Peter J. C. Moses, <a href="/A240672/b240672.txt">Table of n, a(n) for n = 1..2000</a> %H A240672 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. %F A240672 a(n)*A240669(n) = 0. %e A240672 26! = 2^23*3^10*5^6*7^3*11^2*13^2*17*19*23, and the first 4 exponents (23,10,6,3) are evil, so a(13) = 4. %t A240672 Map[Count[First[Split[Map[EvenQ[DigitCount[#,2][[1]]]&,Last[Transpose[FactorInteger[(2*#)!]]&[#]]]]],True]&,Range[75]] (* _Peter J. C. Moses_, Apr 10 2014 *) %Y A240672 Cf. A001969, A240537, A240606, A240619, A240620, A240668, A240669, A240670. %K A240672 nonn %O A240672 1,6 %A A240672 _Vladimir Shevelev_, Apr 10 2014