%I #17 Jan 29 2023 13:34:22
%S 3,7,11,17,29,43,53,71,83,107,127,157,173,199,229,257,293,337,379,401,
%T 457,499,541,577,631,683,733,787,857,911,967,1031,1091,1163,1229,1297,
%U 1373,1447,1553,1601,1697,1787,1867,1973,2029,2129,2213,2339,2411,2503,2617,2707,2819,2927,3041,3137,3251,3457,3491,3607
%N Least odd prime p>n^2 with (n/p) = 1, where ( / ) is the Legendre symbol
%C Conjecture: a(n)<(n+1)^2 for all n>0. (See also A185150.)
%C This conjecture implies that a(1),a(2),a(3),... are pairwise distinct.
%H Zhi-Wei Sun, <a href="/A190898/b190898.txt">Table of n, a(n) for n = 1..10000</a>
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arXiv:1211.1588.
%e a(2)=7 since 7 is the first prime p>2^2 with (2/p) = 1.
%t Do[Do[If[n^2+k>2&&PrimeQ[n^2+k]==True&&JacobiSymbol[n,n^2+k]==1,Print[n," ",n^2+k];Goto[aa]],{k,1,2n}];
%t Label[aa];Continue,{n,1,100}]
%t js[n_]:=Module[{p=NextPrime[n^2]},While[JacobiSymbol[n,p]!=1,p= NextPrime[ p]];p]; Join[{3},Array[js,60,2]] (* _Harvey P. Dale_, Jan 29 2023 *)
%Y Cf. A180150, A014085, A185636.
%K nonn,nice
%O 1,1
%A _Zhi-Wei Sun_, Dec 29 2012