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 A240669 Number of the first odious exponents (A000069) in the prime power factorization of (2n)!. 15
 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, 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, 1, 0, 2, 1, 0, 8, 1, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 0, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: The sequence is unbounded. (This conjecture does not follow from Chen's theorem.) LINKS Peter J. C. Moses, Table of n, a(n) for n = 1..2000 Y.-G. Chen, On the parity of exponents in the standard factorization of n!, J. Number Theory, 100 (2003), 326-331. EXAMPLE 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. MATHEMATICA Map[Count[First[Split[Map[OddQ[DigitCount[#, 2][[1]]]&, Last[Transpose[FactorInteger[(2*#)!]]&[#]]]]], True]&, Range[75]] (* Peter J. C. Moses, Apr 10 2014 *) CROSSREFS Cf. A000069, A240537, A240606, A240619, A240620, A240668. Sequence in context: A190959 A038018 A108658 * A213201 A245843 A188729 Adjacent sequences:  A240666 A240667 A240668 * A240670 A240671 A240672 KEYWORD nonn AUTHOR Vladimir Shevelev, Apr 10 2014 STATUS approved

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Last modified April 22 14:30 EDT 2021. Contains 343177 sequences. (Running on oeis4.)