OFFSET
1,11
COMMENTS
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.
Partial sums of A151763. - Reinhard Zumkeller, Feb 06 2014
LINKS
T. D. Noe, Table of n, a(n) for n=1..30000 (enough terms to show the first dip into negative territory)
Carter Bays and Richard H. Hudson, Zeros of Dirichlet L-Functions and Irregularities in the Distribution of Primes, Mathematics of Computation, 69 (2000) 861-866.
A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.
FORMULA
a(2*n+1) = a(2*n+2) = -A156749(n). - Jonathan Sondow, May 17 2013
MATHEMATICA
a[n_] := Length[Select[Range[3, n, 4], PrimeQ]]-Length[Select[Range[1, n, 4], PrimeQ]]
f[n_]:=Module[{c=Mod[n, 4]}, Which[!PrimeQ[n], 0, c==3, 1, c==1, -1]]; Join[{0, 0}, Accumulate[Array[f, 110, 3]]] (* Harvey P. Dale, Mar 03 2013 *)
PROG
(Haskell)
a066520 n = a066520_list !! (n-1)
a066520_list = scanl1 (+) $ map (negate . a151763) [1..]
-- Reinhard Zumkeller, Feb 06 2014
CROSSREFS
Cf. A156749 Sequence showing Chebyshev bias in prime races (mod 4). [From Daniel Forgues, Mar 26 2009]
Let d be a fundamental discriminant.
Sequences of the form "a(n) = -Sum_{primes p<=n} Kronecker(d,p)" with |d| <= 12: A321860 (d=-11), A320857 (d=-8), A321859 (d=-7), this sequence (d=-4), A321856 (d=-3), A321857 (d=5), A071838 (d=8), A321858 (d=12).
KEYWORD
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), Jan 05 2002
EXTENSIONS
Edited by Dean Hickerson, Mar 05 2002
STATUS
approved