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Search: id:A066520
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| A066520 |
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Number of primes of the form 4m+3 <= n minus number of primes of the form 4m+1 <= n. |
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+0
5
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| 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 2
(list; graph; listen)
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OFFSET
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1,11
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COMMENT
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Although the initial terms are nonnegative, it has been proved that infinitely many terms are negative. The first two are a(26861)=a(26862)=-1. Next, there are 3404 values of n in the range 616841 to 633798 with a(n)<0. Then 27218 values in the range 12306137 to 12382326.
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REFERENCES
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Carter Bays & Richard H. Hudson, Zeros of Dirichlet L-Functions and Irregularities in the Distribution of Primes, Mathematics of Computation, 69 (2000) 861-866.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..30000 (enough terms to show the first dip into negative territory)
Carter Bays & Richard H. Hudson, Zeros of Dirichlet L-Functions and Irregularities in the Distribution of Primes
A. Granville and G. Martin, Prime number races
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FORMULA
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a(n) = A066490(n) - A066339(n)
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MATHEMATICA
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a[n_] := Length[Select[Range[3, n, 4], PrimeQ]]-Length[Select[Range[1, n, 4], PrimeQ]]
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CROSSREFS
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Cf. A066339, A066490, A007350, A051024, A051025.
Cf. A156749 Sequence showing Chebyshev bias in prime races (mod 4). [From Daniel Forgues (squid(AT)zensearch.com), Mar 26 2009]
Sequence in context: A004578 A051031 A111915 this_sequence A088526 A054535 A054534
Adjacent sequences: A066517 A066518 A066519 this_sequence A066521 A066522 A066523
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), Jan 05 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 05 2002
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