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A321865
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a(n) = A321860(prime(n)).
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15
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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, 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, 7, 8, 9, 8, 9, 8, 9, 8, 7, 6, 5, 4, 5, 4, 3, 4, 3, 4, 3, 2
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OFFSET
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1,7
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COMMENTS
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Among the first 10000 terms there are only 32 negative ones.
Please see the comment in A321856 describing "Chebyshev's bias" in the general case.
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LINKS
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FORMULA
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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)).
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EXAMPLE
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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.
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PROG
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(PARI) a(n) = -sum(i=1, n, kronecker(-11, prime(i)))
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CROSSREFS
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Let d be a fundamental discriminant.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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