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# Friedman numbers

A **Friedman number** in a given base is a number that can be written in a nontrivial way using their digits with the basic operations of arithmetic.

Here are a few examples in base 10:

See A036057 for more base 10 Friedman numbers.

A Friedman number is said to be "orderly" when it is possible to put the digits in the expression in the same order as in the usual representation. For example, with , we can rearrange like so: , hence 127 is orderly. See A080035 for more base 10 orderly Friedman numbers.

The concept can also be extended to Roman numerals. For example, LXXXI = IX^{X × X/L}. In many cases, inconvenient "digits" can be "neutralized" by making them into exponents for I, such as in XLIX = L – I^{XX}. See A195419 for more Roman Friedman numbers.

## References

- Erich Friedman, Problem of the Month (August 2000).