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A007351
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Where prime race 4m-1 vs. 4m+1 is tied.
(Formerly M1507)
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23
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2, 5, 17, 41, 461, 26833, 26849, 26863, 26881, 26893, 26921, 616769, 616793, 616829, 616843, 616871, 617027, 617257, 617363, 617387, 617411, 617447, 617467, 617473, 617509, 617531, 617579, 617681, 617707, 617719, 618437, 618521, 618593, 618637
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OFFSET
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1,1
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COMMENTS
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Primes p such that the number of primes <= p of the form 4m-1 is equal to the number of primes <= p of the form 4m+1.
Starting from a(27410)=9103362505753 the sequence includes the 8th sign-changing zone predicted by C. Bays et al. The sequence with the first 8 sign-changing zones contains 419467 terms (see a-file) with a(419467)=9543313015351 as its last term. - Sergei D. Shchebetov, Oct 15 2017
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.
M. Rubinstein and P. Sarnak, Chebyshev’s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, Pages 173-197.
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MATHEMATICA
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Prime@ Position[Fold[Append[#1, #1[[-1]] + If[Mod[#2, 4] == 3, {1, 0}, {0, 1}]] &, {{0, 0}}, Prime@ Range[2, 10^5]], _?(SameQ @@ # &)][[All, 1]] (* Michael De Vlieger, May 27 2018 *)
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PROG
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(PARI) lista(nn) = {nb = 0; forprime(p=2, nn, m = (p % 4); if (m == 1, nb++, if (m == 3, nb--)); if (!nb, print1(p, ", ")); ); } \\ Michel Marcus, Oct 05 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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