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A. Alahmadi, M. Planat, and P. Solé, <a href="https://hal.archives-ouvertes.fr/hal-00650320">Chebyshev's bias and generalized Riemann hypothesis</a>, HAL Id: hal-00650320.

M. Deléglise, P. Dusart, and X. Roblot, <a href="http://dx.doi.org/10.1090/S0025-5718-04-01649-7">Counting Primes in Residue Classes</a>, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp. 1565-1575.

A. Granville, and G. Martin, <a href="https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/granville1.pdf">Prime Number Races</a>, Amer. Math. Monthly 113 (2006), no. 1, 1-33.

M. Rubinstein, and P. Sarnak, <a href="https://projecteuclid.org/euclid.em/1048515870">Chebyshev’s bias</a>, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197.

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Prime Indices of primes at which the prime race 4k-1 vs. 4k+1 is tied at n-th prime.

From Jon E. Schoenfield, Jul 24 2021: (Start)

a(n) is the n-th number m at which the prime race 4k-1 vs. 4k+1 is tied:

.

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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Andrey S. Shchebetov and Sergei D. Shchebetov, <a href="/A038691/a038691-419467.zip">Table of n, a(n) for n = 1..419647 (zipped file)</a>

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Andrey S. Shchebetov and Sergei D. Shchebetov, <a href="/A038691/b038691_1.txt">Table of n, a(n) for n = 1..100000</a> (first 1000 terms from T. D. Noe)

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