cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A298820 #9 May 27 2025 08:41:46
%S A298820 21317046795798,21317046796093,21317046796102,21317046796104,
%T A298820 21317046796154,21317046796159,21317046796172,21317046796185,
%U A298820 21317046796193,21317046796208,21317046796212,21317046796221,21317046796226,21317046796229,21317046796240,21317046796968,21317046796986,21317046796992,21317046797002,21317046797007
%N 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).
%C A298820 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 A298820 Sergei D. Shchebetov, <a href="/A298820/b298820.txt">Table of n, a(n) for n = 1..100000</a>
%H A298820 A. Granville and G. Martin, <a href="https://web.archive.org/web/20240529054811/https://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 A298820 Richard H. Hudson and 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 A298820 M. Rubinstein and 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 A298820 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeQuadraticEffect.html">Prime Quadratic Effect.</a>
%Y A298820 Cf. A295355, A295356, A297449, A297450
%K A298820 nonn
%O A298820 1,1
%A A298820 Andrey S. Shchebetov and _Sergei D. Shchebetov_, Jan 27 2018