login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A207291 Polya-Vinogradov numbers A177865 for primes p == 1 (mod 4). 2
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 (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 == 3 (mod 4) is A207292.
LINKS
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
Sequence in context: A343228 A112778 A080594 * A364443 A194175 A194241
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Feb 16 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 12:21 EDT 2024. Contains 374332 sequences. (Running on oeis4.)