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Friedman number

Number that is the result of operation on its own digits

A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, parentheses, exponentiation, and concatenation.

  • The smallest repdigit in any base that is a Friedman number is found in base 8, and is 33 = 3.
  • The smallest repdigit in base 10 that is known to be a Friedman number is 99999999 = (9 + 9/9) − 9/9. All base 10 Friedman numbers with 7 or fewer digits…
  • It has been proven that repdigits with at least 22 digits are nice Friedman numbers.
  • OEIS sequence A036057 (Friedman number)

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