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.
%I A321862 #18 Nov 19 2023 10:23:46
%S A321862 1,2,2,3,2,3,4,3,4,3,2,3,2,3,4,5,4,3,4,3,4,3,4,3,4,3,4,5,4,5,6,5,6,5,
%T A321862 4,3,4,5,6,7,6,5,4,5,6,5,4,5,6,5,6,5,4,3,4,5,4,3,4,3,4,5,6,5,6,7,6,7,
%U A321862 8,7,8,7,8,9,8,9,8,9,8,7,6,5,4,5,4,5,4
%N A321862 a(n) = A321857(prime(n)).
%C A321862 The first 10000 terms are positive, but conjecturally infinitely many terms should be negative.
%C A321862 The first negative term occurs at a(102091236) = -1. - _Jianing Song_, Nov 08 2019
%C A321862 Please see the comment in A321856 describing "Chebyshev's bias" in the general case.
%H A321862 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev%27s_bias">Chebyshev's bias</a>
%F A321862 a(n) = -Sum_{i=1..n} Legendre(prime(i),5) = -Sum_{primes p<=n} Kronecker(2,prime(i)) = -Sum_{i=1..n} A080891(prime(i)).
%e A321862 prime(25) = 97, Pi(5,1)(97) = Pi(5,4)(97) = 5, Pi(5,2)(97) = Pi(5,3)(97) = 7, so a(25) = 7 + 7 - 5 - 5 = 4.
%o A321862 (PARI) a(n) = -sum(i=1, n, kronecker(5, prime(i)))
%Y A321862 Cf. A080891.
%Y A321862 Let d be a fundamental discriminant.
%Y A321862 Sequences of the form "a(n) = -Sum_{primes p<=n} Kronecker(d,p)" with |d| <= 12: A321860 (d=-11), A320857 (d=-8), A321859 (d=-7), A066520 (d=-4), A321856 (d=-3), A321857 (d=5), A071838 (d=8), A321858 (d=12).
%Y A321862 Sequences of the form "a(n) = -Sum_{i=1..n} Kronecker(d,prime(i))" with |d| <= 12: A321865 (d=-11), A320858 (d=-8), A321864 (d=-7), A038698 (d=-4), A112632 (d=-3), this sequence (d=5), A321861 (d=8), A321863 (d=12).
%K A321862 sign
%O A321862 1,2
%A A321862 _Jianing Song_, Nov 20 2018
%E A321862 Edited by _Peter Munn_, Nov 19 2023