OFFSET
1,11
COMMENTS
Among the first 10000 terms there are only 100 negative ones. See the comments about "Chebyshev's bias" in A320857.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Wikipedia, Chebyshev's bias.
FORMULA
a(n) = -Sum_{i=1..n} Kronecker(prime(i),2) = -Sum_{primes p<=n} Kronecker(2,prime(i)) = -Sum_{i=1..n} A091337(prime(i)).
EXAMPLE
prime(46) = 199, Pi(8,1)(199) = 8, Pi(8,5)(199) = 13, Pi(8,3)(199) = Pi(8,7)(199) = 12, so a(46) = 13 + 12 - 8 - 12 = 5.
MATHEMATICA
a[n_] := -Sum[KroneckerSymbol[-2, Prime[i]], {i, 1, n}];
Array[a, 100] (* Jean-François Alcover, Dec 28 2018, from PARI *)
PROG
(PARI) a(n) = -sum(i=1, n, kronecker(-2, prime(i)))
CROSSREFS
Cf. A188510.
Let d be a fundamental discriminant.
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).
KEYWORD
sign
AUTHOR
Jianing Song, Nov 24 2018
STATUS
approved