A082517 Numbers n such that N(n+1) - N(n) sets a new record, where N(n) = A005349.

1, 10, 11, 26, 28, 32, 83, 102, 143, 561, 716, 1118, 2948, 4194, 5439, 33494, 51544, 61588, 94748, 265336, 800054, 3750017, 6292149, 44194186, 55065654, 61074615, 179838772, 399977785, 497993710, 502602764, 547594831, 1039028518, 14192408715, 14761794180