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 A321865 #17 Nov 19 2023 10:23:38 %S A321865 1,0,-1,0,0,1,2,3,2,3,2,1,2,3,2,1,0,1,0,-1,0,1,2,1,0,1,0,1,2,1,2,3,2, %T A321865 3,4,5,4,3,4,5,4,3,2,3,4,3,4,3,4,3,4,5,6,5,4,5,4,5,6,7,8,9,10,9,8,7,6, %U A321865 7,8,9,8,9,8,9,8,7,6,5,4,5,4,3,4,3,4,3,2 %N A321865 a(n) = A321860(prime(n)). %C A321865 Among the first 10000 terms there are only 32 negative ones. %C A321865 Please see the comment in A321856 describing "Chebyshev's bias" in the general case. %H A321865 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev%27s_bias">Chebyshev's bias</a> %F A321865 a(n) = -Sum_{primes p<=n} Legendre(prime(i),11) = -Sum_{primes p<=n} Kronecker(-11,prime(i)) = -Sum_{i=1..n} A011582(prime(i)). %e A321865 prime(46) = 199. Among the primes <= 199, there are 20 ones congruent to 1, 3, 4, 5, 9 modulo 11 and 23 ones congruent to 2, 6, 7, 8, 10 modulo 11, so a(46) = 23 - 20 = 3. %o A321865 (PARI) a(n) = -sum(i=1, n, kronecker(-11, prime(i))) %Y A321865 Cf. A011582. %Y A321865 Let d be a fundamental discriminant. %Y A321865 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 A321865 Sequences of the form "a(n) = -Sum_{i=1..n} Kronecker(d,prime(i))" with |d| <= 12: this sequence (d=-11), A320858 (d=-8), A321864 (d=-7), A038698 (d=-4), A112632 (d=-3), A321862 (d=5), A321861 (d=8), A321863 (d=12). %K A321865 sign %O A321865 1,7 %A A321865 _Jianing Song_, Nov 20 2018