Quote:
Originally Posted by Hugo1177

You can make this interesting sequance in OEIS
https://oeis.org
If you want the mathematica code for publication :
d = {}; For[i = 1, i <= 326, i++, a = Prime[i];
sol = Solve[x^(2/a)  3 x^(4/a) + 1 == 0, x];
p = ToExpression[
StringCases[ToString[Numerator[RootReduce[(x /. sol[[1]])^2]]],
WordCharacter ..][[1]]]; If[PrimeQ[p], AppendTo[d, a]]]; d