A207291 Polya-Vinogradov numbers A177865 for primes p == 1 (mod 4).

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

Offset: 1

Author

Jonathan Sondow, Feb 16 2012

Keywords

• nonn

Comments

Polya-Vinogradov numbers for all odd primes is A177865, and for primes p == 3 (mod 4) is A207292.

Examples

			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.
		

Crossrefs

Cf. A177865, A207292.

Programs

Mathematica

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]

Formula

a(n) = max_{0

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