Trimorphic number

In mathematics a trimorphic number is a number whose cube (expressed in a given base) ends in the number itself. For example, 4³ = 64, 24³ = 13824, and 249³ = 15438249. The first few trimorphic numbers in base 10 are:

0, 1, 4, 5, 6, 9, 24, 25, 49, 51, 75, 76, 99, 125, 249, 251, 375, 376, 499, 501, 624, 625, 749, 751, 875, 999, 1249, 3751, 4375, 4999, 5001, 5625, 6249, 8751, 9375, 9376, 9999, ... (sequence A033819 in the OEIS)

Every automorphic number is also a trimorphic number, but there are trimorphic numbers which are not automorphic (such as 4, 9 and 24).

Other bases

In base 12, the trimorphic numbers are:

0, 1, 3, 4, 5, 7, 8, 9, Ɛ, 15, 47, 53, 54, 5Ɛ, 61, 68, 69, 75, ᘔ7, Ɛ3, ƐƐ, 115, 253, 368, 369, 4ᘔ7, 5ƐƐ, 601, 715, 853, 854, 969, ᘔᘔ7, ƐƐƐ, 14ᘔ7, 2369, 3853, 3854, 4715, 5ƐƐƐ, 6001, 74ᘔ7, 8368, 8369, 9853, ᘔ715, ƐƐƐƐ, ...

References

Weisstein, Eric W.. "Trimorphic Number". http://mathworld.wolfram.com/TrimorphicNumber.html.