A295355 Values of n for which pi_{24,13}(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).

36826322708, 36826322724, 36826322769, 36826322776, 36826322790, 36826322804, 36826323283, 36826323287, 36826323293, 36826323310, 36826323320, 36826323340, 36826326663, 36826326763, 36826326784, 36826326786, 36826326812, 36826326824, 36826326834, 36826326849

Offset: 1

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 22 2017

Keywords

• nonn

Comments

This is a companion sequence to A295356. The sequence (primes only, without exact n for the first and last terms as well as the number of terms) was found by Bays and Hudson in 1978 (see references). The full sequence up to 10^15 contains 6 sign-changing zones with 2381904 terms in total with A(2381904) = 21113714560133 as the last one.

We found the 7th sign-changing zone between 10^15 and 10^16. It starts with a(2381905) = 245086804685432, ends with a(2792591) = 245853749127075 and contains 410687 terms. - Andrey S. Shchebetov and Sergei D. Shchebetov, Apr 26 2019

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.