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

1,2

Comments

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

Links

Table of n, a(n) for n=1..70.

Formula

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.

Example

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.

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]

Crossrefs

Cf. A177865, A207292.

Sequence in context: A343228 A112778 A080594 * A364443 A194175 A194241

Adjacent sequences: A207288 A207289 A207290 * A207292 A207293 A207294

Keyword

nonn

Author

Jonathan Sondow, Feb 16 2012

Status

approved