A118638 Lesser of a twin-prime pair where both are expressible as the sum of two triangular numbers.

11, 29, 137, 191, 461, 659, 821, 1091, 1721, 2027, 2081, 2711, 3359, 3539, 3917, 6131, 6761, 7589, 7877, 7949, 8219, 9461, 9857, 11351, 12107, 12377, 13691, 13997, 14447, 16139, 16229, 17291, 17417, 17579, 18911, 19469, 19541, 19991, 20549, 20747