cp's OEIS Frontend

A002308 Consecutive quadratic nonresidues mod p.

%I A002308 M0274 N0097 #32 Dec 22 2021 00:09:01
%S A002308 0,1,2,2,3,4,3,4,4,3,4,4,5,5,4,6,5,6,6,6,4,6,7,6,6,5,7,6,10,4,7,8,5,5,
%T A002308 6,7,5,6,6,5,6,6,6,5,5,6,7,7,7,6,7,6,5,7,6,7,9,7,7,7,9,5,7,10,7,7,8,7,
%U A002308 8,6,8,8,9,5,8,8,5,8,9,7,8,12,6,7,10,8,9,9,7,8,11,12,8,8,10,8,7,6,10,10,9,7,10,9,7,6,9
%N A002308 Consecutive quadratic nonresidues mod p.
%C A002308 a(n) is the maximal number of positive reduced quadratic nonresidues which appear consecutively for the n-th prime.
%C A002308 When prime(n) == 3 (mod 4), then a(n) = A002307(n). - _T. D. Noe_, Apr 03 2007
%D A002308 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002308 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002308 T. D. Noe, <a href="/A002308/b002308.txt">Table of n, a(n) for n = 1..10000</a>
%H A002308 A. A. Bennett, <a href="http://dx.doi.org/10.1090/S0002-9904-1926-04211-7">Consecutive quadratic residues</a>, Bull. Amer. Math. Soc., 32 (1926), 283-284.
%t A002308 f[l_, a_] := Module[{A = Split[l], B}, B = Last[Sort[ Cases[A, x : {a ..} :> {Length[x], Position[A, x][[1, 1]]}]]]; {First[B], Length[Flatten[Take[A, Last[B] - 1]]] + 1}]; g[n_] := f[-JacobiSymbol[Range[Prime[n] - 1], Prime[n]], 1][[1]]; g[1] = 0; Table[g[n], {n, 1, 107}] (* _Jean-François Alcover_, Oct 17 2012, after the Mathematica code of _Robert G. Wilson v_ in A002307 *)
%Y A002308 Cf. A002307.
%Y A002308 Cf. A129201
%K A002308 nonn,easy,nice
%O A002308 1,3
%A A002308 _N. J. A. Sloane_
%E A002308 More terms from _David W. Wilson_