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A207292 Polya-Vinogradov numbers A177865 for primes p == 3 (mod 4). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 10 22:36 EDT 2022. Contains 356046 sequences. (Running on oeis4.)