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A240672 Number of the first evil exponents (A001969) in the prime power factorization of (2n)!. 13
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, 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, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 3, 0, 0, 1, 1, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
Conjecture: The sequence is unbounded. (This conjecture does not follow from Chen's theorem.)
LINKS
Y.-G. Chen, On the parity of exponents in the standard factorization of n!, J. Number Theory, 100 (2003), 326-331.
FORMULA
a(n)*A240669(n) = 0.
EXAMPLE
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.
MATHEMATICA
Map[Count[First[Split[Map[EvenQ[DigitCount[#, 2][[1]]]&, Last[Transpose[FactorInteger[(2*#)!]]&[#]]]]], True]&, Range[75]] (* Peter J. C. Moses, Apr 10 2014 *)
CROSSREFS
Sequence in context: A113290 A078442 A175663 * A352288 A243016 A284975
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 10 2014
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)