# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a038691 Showing 1-1 of 1 %I A038691 #41 Jul 25 2021 10:49:59 %S A038691 1,3,7,13,89,2943,2945,2947,2949,2951,2953,50371,50375,50377,50379, %T A038691 50381,50393,50413,50423,50425,50427,50429,50431,50433,50435,50437, %U A038691 50439,50445,50449,50451,50503,50507,50515,50517,50821,50843,50853 %N A038691 Indices of primes at which the prime race 4k-1 vs. 4k+1 is tied. %C A038691 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 %D A038691 Stan Wagon, The Power of Visualization, Front Range Press, 1994, pp. 2-3. %H A038691 Andrey S. Shchebetov and Sergei D. Shchebetov, Table of n, a(n) for n = 1..100000 (first 1000 terms from T. D. Noe) %H A038691 A. Alahmadi, M. Planat and P. SolÃ©, Chebyshev's bias and generalized Riemann hypothesis, HAL Id: hal-00650320. %H A038691 C. Bays and R. H. Hudson, Numerical and graphical description of all axis crossing regions for moduli 4 and 8 which occur before 10^12, International Journal of Mathematics and Mathematical Sciences, vol. 2, no. 1, pp. 111-119, 1979. %H A038691 C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, Zeros of Dirichlet L-functions near the real axis and Chebyshev's bias, J. Number Theory 87 (2001), pp. 54-76. %H A038691 M. DelÃ©glise, P. Dusart and X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp. 1565-1575. %H A038691 A. Granville and G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33. %H A038691 M. Rubinstein and P. Sarnak, Chebyshevâ€™s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197. %H A038691 Andrey S. Shchebetov and Sergei D. Shchebetov, Table of n, a(n) for n = 1..419647 (zipped file) %H A038691 Eric Weisstein's World of Mathematics, Prime Quadratic Effect. %e A038691 From _Jon E. Schoenfield_, Jul 24 2021: (Start) %e A038691 a(n) is the n-th number m at which the prime race 4k-1 vs. 4k+1 is tied: %e A038691 . %e A038691 count %e A038691 ---------- %e A038691 m p=prime(m) p mod 4 4k-1 4k+1 %e A038691 -- ---------- ------- ---- ---- %e A038691 1 2 2 0 = 0 a(1)=1 %e A038691 2 3 -1 1 0 %e A038691 3 5 +1 1 = 1 a(2)=3 %e A038691 4 7 -1 2 1 %e A038691 5 11 -1 3 1 %e A038691 6 13 +1 3 2 %e A038691 7 17 +1 3 = 3 a(3)=7 %e A038691 8 19 -1 4 3 %e A038691 9 23 -1 5 3 %e A038691 10 29 +1 5 4 %e A038691 11 31 -1 6 4 %e A038691 12 37 +1 6 5 %e A038691 13 41 +1 6 = 6 a(4)=13 %e A038691 (End) %t A038691 Flatten[ Position[ FoldList[ Plus, 0, Mod[ Prime[ Range[ 2, 50900 ] ], 4 ]-2 ], 0 ] ] %o A038691 (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 %Y A038691 Cf. A002145, A002313, A007350, A007351, A038698, A051024, A051025, A066520, A096628, A096447, A096448, A199547 %Y A038691 Cf. A156749 Sequence showing Chebyshev bias in prime races (mod 4). - _Daniel Forgues_, Mar 26 2009 %K A038691 nonn %O A038691 1,2 %A A038691 _Hans Havermann_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE