A139490

[Artur]

I was write finally Mathematica programme and execute them. After long 
time computer answer was
A139490 = {1, 4, 6, 7, 8, 10, 14, 16, 18, 22, 26, 38}
Conjecture: This sequence is finite and complete (checked for range n<=200
and m<=500)
finding all pairs {n,m} in range (checked for range n<=200 and m<=500)
n={1, 4, 4, 6, 6, 7, 8, 8, 10, 10, 10, 14, 14, 14, 16, 18, 22, 22, 26, 
38, 38}
m={3, 9, 12, 8, 16, 15, 45, 60, 24, 48, 72, 24, 48, 72, 21, 40, 120, 
240, 168, 120, 240}

That mean that existed only 12 such values n every prime represented by 
symmetrical binary forms of the kind x^2 + n*x*y + y^2 can be also be 
represented by  form z^2+m t^2

Artur