
COMMENTS

From Bruno Berselli, Aug 26 2015: (Start)
After 1, m is always even (for m odd 4^m+11 is divisible by 5).
Let m = 2*h. For h = 3*k+1, 9*k+3, 11*k+2, 11*k+8, 13*k+8, 19*k+6, 23*k+10, 23*k+14 and 29*k+28, 4^m+11 is divisible by 9, 37, 89, 23, 53, 229, 47, 1013 and 59, respectively. (End)
All terms appear to be of the form 3*k+1.  Dhilan Lahoti, Aug 31 2015
12702 is the first counterexample to Dhilan Lahoti's conjecture: 12702 = 3*4234.  Bruno Berselli, Feb 02 2017
a(14) > 300,000.  Robert Price, Mar 18 2017
