A207292 Polya-Vinogradov numbers A177865 for primes p == 3 (mod 4).

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, 22, 21, 21, 22, 13, 14, 25, 14, 17, 27, 19, 15, 27, 27, 30, 30, 18, 17, 21, 33, 19, 27, 17, 33, 19, 20, 27, 20, 22, 36, 26, 18, 26, 19, 36, 33, 23, 19, 41, 28, 23

Offset

1,2

Comments

Polya-Vinogradov numbers for all odd primes is A177865, and for primes p == 1 (mod 4) is A207291.

Links

Table of n, a(n) for n=1..68.

Formula

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.

Example

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.

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, 3]

Crossrefs

Cf. A177865, A207291.

Sequence in context: A349669 A023156 A051599 * A064464 A094585 A183322

Adjacent sequences: A207289 A207290 A207291 * A207293 A207294 A207295

Keyword

nonn

Author

Jonathan Sondow, Feb 16 2012

Status

approved