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%I #16 Nov 19 2023 10:23:23
%S 0,0,1,2,1,0,1,2,1,2,3,2,3,4,3,4,3,2,3,2,1,2,1,2,1,2,3,2,1,2,3,2,3,4,
%T 5,6,5,6,5,6,5,4,3,2,3,4,5,6,5,4,5,4,3,2,3,2,3,4,3,4,5,6,7,6,5,6,7,6,
%U 5,4,5,4,5,4,5,4,5,4,5,4,3,2,1,0,1,0,1
%N a(n) = A321858(prime(n)).
%C Among the first 10000 terms there are only 291 negative ones, with the earliest one being a(6181) = -1. See the comments about "Chebyshev's bias" in A321858.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev%27s_bias">Chebyshev's bias</a>
%F a(n) = -Sum_{primes p<=n} Kronecker(12,prime(i)) = -Sum_{i=1..n} A110161(prime(i)).
%e prime(25) = 97, Pi(12,1)(97) = 5, Pi(12,5)(97) = Pi(12,7)(97) = Pi(12,11)(97) = 6, so a(25) = 6 + 6 - 5 - 6 = 1.
%o (PARI) a(n) = -sum(i=1, n, kronecker(12, prime(i)))
%Y Cf. A110161.
%Y Let d be a fundamental discriminant.
%Y 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 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), A321862 (d=5), A321861 (d=8), this sequence (d=12).
%K sign
%O 1,4
%A _Jianing Song_, Nov 20 2018
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