Equidigital number

Demonstration, with Cuisenaire rods, that the composite number 10 is equidigital: 10 has two digits, and 2×5 has two digits (1 is excluded)

An equidigital number is a natural number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. For example, in base-10 arithmetic 1, 2, 3, 5, 7, and 10 (2×5) are equidigital numbers (sequence A046758 in the OEIS). All prime numbers are equidigital numbers in any base.

A number that is either equidigital or frugal is said to be economical.

References

R.G.E. Pinch (1998), Economical Numbers.

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Divisibility-based sets of integers
Overview	Integer factorization Divisor Unitary divisor Divisor function Prime factor Fundamental theorem of arithmetic Arithmetic number
Factorization forms	Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular Rough Unusual
Constrained divisor sums	Perfect Almost perfect Quasiperfect Multiply perfect Hemiperfect Hyperperfect Superperfect Unitary perfect Semiperfect Practical Erdős–Nicolas
With many divisors	Abundant Primitive abundant Highly abundant Superabundant Colossally abundant Highly composite Superior highly composite Weird
Aliquot sequence-related	Untouchable Amicable Sociable Betrothed
Other sets	Deficient Friendly Solitary Sublime Harmonic divisor Frugal Equidigital Extravagant

Equidigital number

See also

References