cp's OEIS Frontend

A235709 Least prime p < prime(n) with 2^p - 1 a quadratic residue modulo prime(n), or 0 if such a number does not exist.

%I A235709 #8 Apr 20 2014 19:57:58
%S A235709 0,0,0,0,2,2,7,3,2,3,3,2,5,5,2,3,2,2,7,2,2,5,2,23,2,5,3,2,2,3,5,2,3,3,
%T A235709 3,5,2,11,2,5,2,2,2,2,3,3,11,3,2,2,3,2,2,2,5,2,7,3,2,3,3,5,3,2,2,3,5,
%U A235709 2,2,2,7,2,3,2,7,2,3,2,3,2,2,2,2,2,3,2,3,2,11,5,2,2,5,2,5,2,7,5,3,2
%N A235709 Least prime p < prime(n) with 2^p - 1 a quadratic residue modulo prime(n), or 0 if such a number does not exist.
%C A235709 Conjecture: a(n) > 0 for all n > 4.
%C A235709 We have verified this for all n = 5, ..., 10^8.
%C A235709 Note that the conjecture in A234972 implies that for any prime p > 3 there is a prime q < p with 2^q - 1 a quadratic nonresidue modulo p.
%H A235709 Zhi-Wei Sun, <a href="/A235709/b235709.txt">Table of n, a(n) for n = 1..10000</a>
%e A235709 a(8) = 3 since 2^3 - 1 = 7 is a quadratic residue modulo prime(8) = 19, but 2^2 - 1 = 3 is not.
%t A235709 Do[Do[If[JacobiSymbol[2^(Prime[k])-1,Prime[n]]==1,Print[n," ",Prime[k]];Goto[aa]],{k,1,n-1}];Print[n," ",0];Label[aa];Continue,{n,1,100}]
%Y A235709 Cf. A000040, A001348, A234972.
%K A235709 nonn
%O A235709 1,5
%A A235709 _Zhi-Wei Sun_, Apr 20 2014