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%I #11 Mar 30 2012 19:00:10
%S 1,2,3,3,5,6,5,8,9,6,10,10,9,10,9,10,15,9,14,9,18,15,19,18,12,15,15,
%T 22,21,21,22,13,14,25,14,17,27,19,15,27,27,30,30,18,17,21,33,19,27,17,
%U 33,19,20,27,20,22,36,26,18,26,19,36,33,23,19,41,28,23
%N Polya-Vinogradov numbers A177865 for primes p == 3 (mod 4).
%C Polya-Vinogradov numbers for all odd primes is A177865, and for primes p == 1 (mod 4) is A207291.
%F a(n) = max_{0<k<p} |sum_{i=1..k} L(i/p)|, where p is the n-th prime == 3 (mod 4) and L(i/p) is the Legendre symbol.
%e The 2nd prime == 3 (mod 4) is 7 = prime(4), and A177865(4) = 2 (not 3, because the offset of A177865 is 2, not 1), so a(2) = 2.
%t T = Table[Max[Table[Abs[Sum[JacobiSymbol[i, Prime[n]], {i, 1, k}]], {k, 1, Prime[n] - 1}]], {n, 2, 200}]; P = Table[Mod[Prime[n], 4], {n, 2, 200}]; Pick[T, P, 3]
%Y Cf. A177865, A207291.
%K nonn
%O 1,2
%A _Jonathan Sondow_, Feb 16 2012
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