An equidigital number $n$ is an integer with a base $b$ representation of $k$ digits for which the prime factorization uses exactly $k$ digits (with repeated prime factors grouped with exponents and the digits of those exponents counted whenever greater than 1). Regardless of the base, all primes are equidigital. The first few composite equidigital numbers in base 10 are 10, 14, 15, 16, 21, 25, 27, 32, 35, 49, 64, 81, 105, 106, 111, 112, 115, 118, 119, 121, 122, 123, 129, 133, 134, 135, etc.

Bibliography

1

D. Darling, ``Economical number'' in The Universal Book of Mathematics: From Abracadabra To Zeno's paradoxes. Hoboken, New Jersey: Wiley (2004)

2

B. R. Santos, ``Problem 2204. Equidigital Representation.'' J. Recr. Math. 27 (1995): 58 - 59.