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Hereditary Representation

The representation of a number as a sum of powers of a Base $b$, followed by expression of each of the exponents as a sum of powers of $b$, etc., until the process stops. For example, the hereditary representation of 266 in base 2 is

$\displaystyle 266$ $\textstyle =$ $\displaystyle 2^8+2^3+2$  
  $\textstyle =$ $\displaystyle 2^{2^{2+1}}+2^{2+1}+2.$  

See also Goodstein Sequence

© 1996-9 Eric W. Weisstein