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
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, Conjectures involving primes and quadratic forms, arXiv:1211.1588.
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
Zhi-Wei Sun, Dec 29 2012
STATUS
approved