All numbers n that solve x^2 = 165 * 2^n + 26404.
0, 5, 7, 8, 10, 12
1
Ulas finds equations having six solutions.
T. D. Noe, Plot of 6 terms
Maciej Ulas, Some experiments with Ramanujan-Nagell type Diophantine equations, arXiv 1409.8132 (Sep 29 2014)
(Mma) Select[Range[0, 1000], IntegerQ[Sqrt[165*2^# + 26404]] &]
Cf. S000270.
nonn,full
T. D. Noe, Oct 01 2014