

A190898


Least odd prime p>n^2 with (n/p) = 1, where ( / ) is the Legendre symbol


1



3, 7, 11, 17, 29, 43, 53, 71, 83, 107, 127, 157, 173, 199, 229, 257, 293, 337, 379, 401, 457, 499, 541, 577, 631, 683, 733, 787, 857, 911, 967, 1031, 1091, 1163, 1229, 1297, 1373, 1447, 1553, 1601, 1697, 1787, 1867, 1973, 2029, 2129, 2213, 2339, 2411, 2503, 2617, 2707, 2819, 2927, 3041, 3137, 3251, 3457, 3491, 3607
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OFFSET

1,1


COMMENTS

Conjecture: a(n)<(n+1)^2 for all n>0. (See also A185150.)
This conjecture implies that a(1),a(2),a(3),... are pairwise distinct.


LINKS



EXAMPLE

a(2)=7 since 7 is the first prime p>2^2 with (2/p) = 1.


MATHEMATICA

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}];
Label[aa]; Continue, {n, 1, 100}]
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 *)


CROSSREFS



KEYWORD

nonn,nice


AUTHOR



STATUS

approved



