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A038691
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Indices of primes at which the prime race 4k-1 vs. 4k+1 is tied.
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23
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1, 3, 7, 13, 89, 2943, 2945, 2947, 2949, 2951, 2953, 50371, 50375, 50377, 50379, 50381, 50393, 50413, 50423, 50425, 50427, 50429, 50431, 50433, 50435, 50437, 50439, 50445, 50449, 50451, 50503, 50507, 50515, 50517, 50821, 50843, 50853
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OFFSET
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1,2
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COMMENTS
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Starting from a(27410) = 316064952537 the sequence includes the 8th sign-changing zone predicted by C. Bays et al back in 2001. The sequence with the first 8 sign-changing zones contains 419467 terms (see a-file) with a(419467) = 330797040309 as its last term. - Sergei D. Shchebetov, Oct 16 2017
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REFERENCES
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Stan Wagon, The Power of Visualization, Front Range Press, 1994, pp. 2-3.
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LINKS
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A. Granville and G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
M. Rubinstein and P. Sarnak, Chebyshev’s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197.
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EXAMPLE
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a(n) is the n-th number m at which the prime race 4k-1 vs. 4k+1 is tied:
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count
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m p=prime(m) p mod 4 4k-1 4k+1
-- ---------- ------- ---- ----
1 2 2 0 = 0 a(1)=1
2 3 -1 1 0
3 5 +1 1 = 1 a(2)=3
4 7 -1 2 1
5 11 -1 3 1
6 13 +1 3 2
7 17 +1 3 = 3 a(3)=7
8 19 -1 4 3
9 23 -1 5 3
10 29 +1 5 4
11 31 -1 6 4
12 37 +1 6 5
13 41 +1 6 = 6 a(4)=13
(End)
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MATHEMATICA
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Flatten[ Position[ FoldList[ Plus, 0, Mod[ Prime[ Range[ 2, 50900 ] ], 4 ]-2 ], 0 ] ]
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PROG
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(PARI) lista(nn) = {nbp = 0; nbm = 0; forprime(p=2, nn, if (((p-1) % 4) == 0, nbp++, if (((p+1) % 4) == 0, nbm++)); if (nbm == nbp, print1(primepi(p), ", ")); ); } \\ Michel Marcus, Nov 20 2016
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CROSSREFS
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Cf. A002145, A002313, A007350, A007351, A038698, A051024, A051025, A066520, A096628, A096447, A096448, A199547
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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