Primes p congruent to 1 or 5 for which sum_{1..(p-1)/4} Legendre(i/p) reaches a new maximum.
5, 17, 29, 41, 89, 101, 257, 269, 461, 521, 701, 761, 941, 1109, 1361, 1889, 2141, 2609, 3449, 4241, 4289, 5081, 5381, 6569, 7229, 7829, 8069, 8609, 9749, 10601, 10709, 13109, 14621, 15461, 19421, 19841, 20789, 21089, 23201, 29669, 31121, 32009, 33809, 36209
1
Here Legendre(i/p) is the Legendre symbol.
T. D. Noe, Plot of 100 terms
T. D. Noe, Table of 100 terms
Eric W. Weisstein, MathWorld: Legendre Symbol
(Mma) t = {}; mx = 0; n = 0; While[Length[t] < 50, n++; p = Prime[n]; If[MemberQ[{1, 5}, Mod[p, 8]], s = Plus @@ JacobiSymbol[Range[(p - 1)/4], p]; If[s > mx, mx = s; AppendTo[t, {p, s}]]]]; Transpose[t][[1]]
Cf. S000752, S000753, S000755.
nonn,hard
T. D. Noe, Nov 20 2015