All numbers n that solve x^2 = 57 * 2^n + 117440512.
0, 14, 16, 20, 24, 25
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[57*2^# + 117440512]] &]
Cf. S000271.
nonn,full
T. D. Noe, Oct 01 2014