A298820 - OEIS

A298820

Values of n for which pi_{24,19}(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).

%I #5 Feb 03 2018 12:53:27

%S 21317046795798,21317046796093,21317046796102,21317046796104,

%T 21317046796154,21317046796159,21317046796172,21317046796185,

%U 21317046796193,21317046796208,21317046796212,21317046796221,21317046796226,21317046796229,21317046796240,21317046796968,21317046796986,21317046796992,21317046797002,21317046797007

%N Values of n for which pi_{24,19}(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).

%C This is a companion sequence to A298821 and the first discovered for pi_{24,19}(p) - pi_{24,1}(p) prime race. The full sequence up to 10^15 contains 5 sign-changing zones with 3436990 terms in total with A(3436990) = 23049274819456 as the last one.

%H Sergei D. Shchebetov, <a href="/A298820/b298820.txt">Table of n, a(n) for n = 1..100000</a>

%H A. Granville, G. Martin, <a href="https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/granville1.pdf">Prime Number Races</a>, Amer. Math. Monthly 113 (2006), no. 1, 1-33.

%H Richard H. Hudson, Carter Bays, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002194864">The appearance of tens of billion of integers x with pi_{24, 13}(x) < pi_{24, 1}(x) in the vicinity of 10^12</a>, Journal für die reine und angewandte Mathematik, 299/300 (1978), 234-237. MR 57 #12418.

%H M. Rubinstein, P. Sarnak, <a href="https://projecteuclid.org/euclid.em/1048515870">Chebyshev’s bias</a>, Experimental Mathematics, Volume 3, Issue 3, 1994, Pages 173-197.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeQuadraticEffect.html">Prime Quadratic Effect.</a>

%Y Cf. A295355, A295356, A297449, A297450

%K nonn

%O 1,1

%A Andrey S. Shchebetov and _Sergei D. Shchebetov_, Jan 27 2018