A094873 n! has a triangular number of digits.
0, 1, 2, 3, 5, 6, 9, 13, 17, 32, 38, 44, 65, 106, 125, 135, 156, 178, 201, 213, 278, 292, 306, 335, 350, 381, 413, 446, 463, 480, 570, 589, 608, 647, 667, 687, 728, 749, 770, 880, 996, 1020, 1044, 1169, 1247, 1300, 1327, 1354, 1437, 1551, 1669, 1699, 1760
Offset: 0
Programs
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Mathematica
Select[Range[0,1800],OddQ[Sqrt[1+8 IntegerLength[#!]]]&] (* Harvey P. Dale, Aug 07 2023 *)