A297449 Values of n for which pi_{24,17}(p_n) - pi_{24,1}(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).

18687728175380, 18687728175387, 18687728175395, 18687728175515, 18687728175520, 18687728175587, 18687728175592, 18687728175626, 18687728175698, 18687728175707, 18687728175715, 18687728175726, 18687728175738, 18687728175762, 18687728176789, 18687728176820, 18687728176831, 18687728176844, 18687728176846, 18687728185530

Offset: 1

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 27 2018

Keywords

• nonn

Comments

This is a companion sequence to A297450 and the first discovered for pi_{24,17}(p) - pi_{24,1}(p) prime race. The full sequence up to 10^15 contains 3 sign-changing zones with 963922 terms in total with A(963922) = 23241097440243 as the last one.

Links

• Sergei D. Shchebetov, Table of n, a(n) for n = 1..100000
• A. Granville and G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
• Richard H. Hudson and Carter Bays, The appearance of tens of billion of integers x with pi_{24, 13}(x) < pi_{24, 1}(x) in the vicinity of 10^12, Journal für die reine und angewandte Mathematik, 299/300 (1978), 234-237. MR 57 #12418.
• 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.

Crossrefs

Cf. A295355, A295356.