A240669 Number of the first odious exponents (A000069) in the prime power factorization of (2n)!.

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

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