The first two such pair are (1913, 1931) and (18379, 18397), while the first triplet, quadruple and quintuple are (11117123, 11117213, 11117321), 6607882000+(123,213,231,321) and 20847942560000+(0791,0917,0971,1097).

J.K.Andersen has determined that the smallest triple using only two distinct digits is 1311111133113111000 + (133, 313, 331). Among other results, he also found a 74-digit 9-tuple.

Every number greater than 119639 can be written as the sum of Ormiston numbers.

The first Ormiston pairs are (1913, 1931), (18379, 18397), (19013, 19031), (25013, 25031), (34613, 34631), (35617, 35671), (35879, 35897), (36979, 36997), (37379, 37397), (37813, 37831), (40013, 40031) more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here