Equivalently, lower member of consecutive terms of A249551.

Other terms include 50225, 115785, 130974, 160474, 241366, 292774, 297689, 359106, 66885, 375254, 512974, 542654, 626354, 630002, 668205, 670074, 755825, 763637, 806518, 807274, 877162, 902565, 944414, but other terms may also be in this range. - Robert Price, May 24 2019

10845 is in the sequence because A000001(10845) = A000001(10846) = 8, 32769 is in the sequence because A000001(32769) = A000001(32770) = 8 and 47294 is in the sequence because A000001(47294) = A000001(47295) = 8.

MATHEMATICA

Select[Range[10^6], (FiniteGroupCount[#] == 8 && FiniteGroupCount[# + 1] == 8) &] (* A current limit in Mathematica is such that some orders >2047 may not be evaluated. *) (* Robert Price, May 24 2019 *)