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Vell mentioned the idea of starting a new Bignum Bakeoff.  I hope that happens, but here is a closely related problem that could serve as an appetizer to the big contest.

Namely, write a program using the shortest number of characters that implements a function with growth rate comparable to \(f_{\varepsilon_0} (n)\). My first interest is using the language C, but you can program in any language you want - each language will be a different category of course.

Some rules:

1. The program must return a number at least \(f_{\omega^{\omega^{\omega^\omega}}}(4)\).  (Nothing really special about this number, just wanted to pick a number big enough to require an epsilon_0 function but not much bigger.)

2. It is assumed that every language has integer types that can take arbitrary values.  Of course, you cannot refer to MAXINT or the like.

3. The winner (for a given language) is the acceptable program with the fewest number of non-whitespace characters (In homage to the original BAKEOFF, I am not counting whitespace characters.)

Also, please indicate which langauge you are using.

More rules will probably be created as issues come up.


Looking forward to seeing some entries!

Current Leading Entries

Python:

  • Sait2000, 83 characters (using Goodstein sequences)
  • Deedlit11, 91 characters (using Goodstein sequences)
  • Deedlit11/Wythagoras, 102 characters (using Goodstein sequences)
  • Vel!, 110 characters (using Beklemishev's worms)

C:

  • Deedlit11, 101 characters (using Goodstein sequences)
  • Vel!, 121 characters (using Goodstein sequences)
  • Deedlit11, 129 characters (using Goodstein sequences)
  • Vel!, 150 characters (using Beklemishev's worms)
  • Kyodaisuu, 163 characters (using Bashicu's primitive sequences)

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