A297447
Values of n for which pi_{8,5}(p_n) - pi_{8,1}(p_n) = -1, where p_n is the n-th prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).
Original entry on oeis.org
30733704, 30733708, 30733714, 30733726, 30733729, 30733733, 30733743, 30733762, 30733764, 30733777, 30733781, 30733796, 30733853, 30733857, 30733860, 30733866, 30733880, 30733887, 30733890, 30734262
Offset: 1
- Sergei D. Shchebetov, Table of n, a(n) for n = 1..100000
- 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.
- 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.
- M. Deléglise, P. Dusart, and X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp.1565-1575.
- 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, Pages 173-197.
- Eric Weisstein's World of Mathematics, Prime Quadratic Effect.
Cf.
A007350,
A007351,
A038691,
A051024,
A051025,
A066520,
A096628,
A096447,
A096448,
A199547,
A275939,
A295354,
A379643,
A379989.
-
from sympy import nextprime; p, r1, r5 = 1, 0, 0
for n in range(1, 30734263):
p = nextprime(p); r = p%8
if r == 1: r1 += 1
elif r == 5: r5 += 1
if r in {1, 5} and r1 == r5 + 1: print(n, end = ', ') # Ya-Ping Lu, Jan 08 2025
A295353
Values of n for which pi_{8,7}(p_n) - pi_{8,1}(p_n) = -1, where p_n is the n-th prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).
Original entry on oeis.org
6035005477560, 6035005477596, 6035005477608, 6035005477618, 6035005477620, 6035005477623, 6035005477632, 6035005478719, 6035005478725, 6035005478730, 6035005478822, 6035005478826, 6035005478829, 6035005478863, 6035005478866, 6035005478874, 6035005479026, 6035005479132, 6035005479158, 6035005479163
Offset: 1
- Andrey S. Shchebetov and Sergei D. Shchebetov, Table of n, a(n) for n = 1..100000
- A. Alahmadi, M. Planat, and P. Solé, Chebyshev's bias and generalized Riemann hypothesis, HAL Id: hal-00650320.
- 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.
- 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.
- M. Deléglise, P. Dusart, and X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp.1565-1575.
- 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, Pages 173-197.
- Eric Weisstein's World of Mathematics, Prime Quadratic Effect.
Cf.
A007350,
A007351,
A038691,
A051024,
A051025,
A066520,
A096628,
A096447,
A096448,
A199547,
A275939,
A295354
Showing 1-2 of 2 results.
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