OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
L. Carlitz, The coefficients of the lemniscate function, Math. Comp., 16 (1962), 475-478.
EXAMPLE
From Seiichi Manyama, Sep 26 2016: (Start)
Let p be a prime of the form 4k+1 so that p = a^2 + b^2.
We take a odd and such that a = b + 1 (mod 4).
p = 5 = (-1)^2 + 2^2 and -1 = 2 + 1 (mod 4). So a(1) = -1.
p = 13 = 3^2 + 2^2 and 3 = 2 + 1 (mod 4). So a(2) = 3.
p = 17 = 1^2 + 4^2 and 1 = 4 + 1 (mod 4). So a(3) = 1.
p = 29 = 5^2 + 2^2 and -5 = 2 + 1 (mod 4). So a(4) = -5.
(End)
MATHEMATICA
Map[-Sum[JacobiSymbol[x^3 - x, #], {x, 0, # - 1}] &, Select[Prime@ Range@ 155, Mod[#, 4] == 1 &]]/2 (* Michael De Vlieger, Sep 26 2016, after Jean-François Alcover at A002172 *)
PROG
(PARI) a002172(n) = {my(m, c); if(n<1, 0, c=0; m=0; while(c<n, m++; if(isprime(m)& m%4==1, c++)); -sum(x=0, m-1, kronecker(x^3-x, m)))}
a(n) = a002172(n)/2; \\ Altug Alkan, Sep 27 2016
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Offset changed to 1 to match A002172, Joerg Arndt, Sep 27 2016
STATUS
approved