A297450 Primes p for which pi_{24,17}(p) - pi_{24,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

617139273158713, 617139273159121, 617139273159337, 617139273163729, 617139273163793, 617139273165889, 617139273166121, 617139273167057, 617139273169273, 617139273169513, 617139273169729, 617139273170137, 617139273170401, 617139273171217, 617139273206009, 617139273206993, 617139273207449, 617139273207929, 617139273208001, 617139273504913

Offset: 1

Author

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

Keywords

• nonn

Comments

This is a companion sequence to A297449 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) = 772739867710897 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.