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Friedman Number


A Friedman number is a positive integer expressible nontrivially using all of its own decimal digits exactly once, together with plus, minus, times, division, exponentiation, parentheses, and concatenation (Friedman 2000). The digits may be rearranged, but merely writing the original number is excluded. For example,

 25=5^2,

and other examples are 121=11^2, 127=-1+2^7, and 343=(3+4)^3.

Inserting decimal points or using additional operations such as square root or factorial does not belong to the standard definition (Friedman 2000).


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References

Friedman, E. "Problem of the Month (August 2000)." https://erich-friedman.github.io/mathmagic/0800.html.Numberphile. "Friedman Numbers." Sep. 12, 2014. https://www.youtube.com/watch?v=I7v2wAXFQpc.

Cite this as:

Weisstein, Eric W. "Friedman Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FriedmanNumber.html

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