OFFSET
1,1
COMMENTS
No more terms below 10^10.
Conjecture: No term is greater than 3119. In other words, for any prime p > 3120, there is a Pythagorean triple (2*a,a^2-1,a^2+1) with 2*a, a^2-1 and a^2+1 in the set {0 < r < p: r is a quadratic nonresidue modulo p}.
See also A344620 for a similar conjecture.
EXAMPLE
a(5) = 13. The prime 11 is not a term since 2*3 = 6, 3^2-1 = 8 and 3^2+1 = 10 belong to the set {0 < r < 11: r is a quadratic nonresidue modulo 11} = {2, 6, 7, 8, 10}.
MATHEMATICA
tab={}; Do[p:=p=Prime[k]; Do[If[JacobiSymbol[2a, p]==-1&&JacobiSymbol[a^2-1, p]==-1&&JacobiSymbol[a^2+1, p]==-1, Goto[aa]], {a, 1, Sqrt[p-2]}]; tab=Append[tab, p]; Label[aa], {k, 1, 450}]; Print[tab]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 24 2021
STATUS
approved