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A038698
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Excess of 4k-1 primes over 4k+1 primes, beginning with prime 2.
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28
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0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 3, 4, 3, 4, 5, 4, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 6
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OFFSET
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1,5
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COMMENTS
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a(n) < 0 for infinitely many values of n. - Benoit Cloitre, Jun 24 2002
First negative value is a(2946) = -1, which is for prime 26861. - David W. Wilson, Sep 27 2002
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REFERENCES
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Stan Wagon, The Power of Visualization, Front Range Press, 1994, p. 2.
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LINKS
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FORMULA
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a(n) = Sum_{k=2..n} (-1)^((prime(k)+1)/2). - Benoit Cloitre, Jun 24 2002
a(n) = (Sum_{k=1..n} prime(k) mod 4) - 2*n (assuming that x mod 4 > 0). - Thomas Ordowski, Sep 21 2012
(End)
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MAPLE
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ans:=[0]; ct:=0; for n from 2 to 2000 do
p:=ithprime(n); if (p mod 4) = 3 then ct:=ct+1; else ct:=ct-1; fi;
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MATHEMATICA
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FoldList[Plus, 0, Mod[Prime[Range[2, 110]], 4] - 2]
Join[{0}, Accumulate[If[Mod[#, 4]==3, 1, -1]&/@Prime[Range[2, 110]]]] (* Harvey P. Dale, Apr 27 2013 *)
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PROG
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(PARI) for(n=2, 100, print1(sum(i=2, n, (-1)^((prime(i)+1)/2)), ", "))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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