A179073 A179071 for p == 1 (mod 4).

-2, -18, -4, -70, -882, -32, -182, -29718, -1068, -500, -5604, -4030, -8890182, -776, -1744, -113582, -4832118, -1118, -1111225770, -1764132, -11018, -20000849130, -23156, -71011068, -16432, -2205718, -8920484118, -1063532

Offset: 1

Author

Jonathan Sondow and Wadim Zudilin, Jun 29 2010

Keywords

• sign

Comments

It appears that a(n) is negative and even. (Added Aug 28 2011: This conjecture has been proved by Maxim Vsemirnov.)

Links

• M. Vsemirnov, On R. Chapman's "evil determinant": case p == 1 (mod 4), arXiv preprint arXiv:1108.4031 [math.NT], 2011-2012.

Crossrefs

Cf. A179071, A179072, A179074.

Programs

Mathematica

a71[p_] := Module[{k}, k = (p-1)/2; Det @ Table[JacobiSymbol[j-i, p], {i, 1, k+1}, {j, 1, k+1}]];
a71 /@ Select[Range[1, 301, 4], PrimeQ] (* Jean-François Alcover, Dec 05 2018 *)