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Friedman numbers

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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 = IXX × X/L. In many cases, inconvenient "digits" can be "neutralized" by making them into exponents for I, such as in XLIX = L – IXX. See A195419 for more Roman Friedman numbers.