A295356 Primes p for which pi_{24,13}(p) - pi_{24,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

978412359121, 978412359637, 978412360813, 978412360957, 978412361293, 978412361713, 978412374613, 978412374673, 978412374817, 978412375441, 978412375597, 978412376197, 978412466749, 978412469581, 978412470193, 978412470241, 978412470877, 978412471081, 978412471357, 978412471789

Offset: 1

Author

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

Keywords

• nonn

Comments

This is a companion sequence to A295355. The sequence (without exact 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) = 699914738212849 as the last one.

We found the 7th sign-changing zone between 10^15 and 10^16. It starts with A(2381905) = 8744052767229817, ends with A(2792591) = 8772206355445549 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.