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

%I

%S -2,-18,-4,-70,-882,-32,-182,-29718,-1068,-500,-5604,-4030,-8890182,

%T -776,-1744,-113582,-4832118,-1118,-1111225770,-1764132,-11018,

%U -20000849130,-23156,-71011068,-16432,-2205718,-8920484118,-1063532

%N A179071 for p == 1 (mod 4).

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

%H M. Vsemirnov, <a href="http://arxiv.org/abs/1108.4031">On R. Chapman's "evil determinant": case p == 1 (mod 4)</a>, arXiv preprint arXiv:1108.4031 [math.NT], 2011-2012.

%t a71[p_] := Module[{k}, k = (p-1)/2; Det @ Table[JacobiSymbol[j-i, p], {i, 1, k+1}, {j, 1, k+1}]];

%t a71 /@ Select[Range[1, 301, 4], PrimeQ] (* _Jean-Fran├žois Alcover_, Dec 05 2018 *)

%Y Cf. A179071, A179072, A179074.

%K sign

%O 1,1

%A _Jonathan Sondow_ and _Wadim Zudilin_, Jun 29 2010

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Last modified November 27 04:52 EST 2021. Contains 349345 sequences. (Running on oeis4.)