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A207291
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Polya-Vinogradov numbers A177865 for primes p == 1 (mod 4).
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2
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1, 2, 2, 3, 4, 4, 5, 4, 5, 6, 6, 7, 6, 6, 7, 7, 8, 9, 7, 8, 11, 9, 10, 8, 10, 11, 14, 10, 11, 11, 13, 12, 12, 12, 16, 12, 12, 12, 12, 11, 14, 13, 12, 15, 15, 16, 14, 19, 16, 16, 16, 14, 20, 16, 15, 21, 16, 16, 19, 17, 15, 18, 22, 20, 17, 17, 18, 16, 17, 17
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OFFSET
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1,2
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COMMENTS
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Polya-Vinogradov numbers for all odd primes is A177865, and for primes p == 3 (mod 4) is A207292.
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LINKS
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FORMULA
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a(n) = max_{0<k<p} |sum_{i=1..k} L(i/p)|, where p is the n-th prime == 1 (mod 4) and L(i/p) is the Legendre symbol.
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EXAMPLE
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The 3rd prime == 1 (mod 4) is 17 = prime(7), and A177865(7) = 2 (not 3, because the offset of A177865 is 2, not 1), so a(3) = 2.
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MATHEMATICA
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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, 1]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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