Flak Function

In this page, I will compute Flak() function, made by Nish, which defined as any Flak(n) is the largest number evaluated from Brain-Flak with 2n characters inside of (_). But what is Brain-Flak?

Brain-Flak?!

Brain-Flak is a language that created by DJMcMayhem and Wheatwizard in GitHub. The code ignores all characters excluding (, ), [, ], {, }, <, and >; then check the brackets, then run it. There are 8 commands, running from left-to-right order.

  • () - Evaluate 1.
  • [] - Evaluate the height of the active stack.
  • {} - Pop the top of the active stack then evaluate it.
  • <> - Toggle the active stack to other stack. There are 2 stacks in Brain-Flak.
  • (A) - Evaluate the sum of evaluated numbers in A then push it to the top of the active stack.
  • [A] - Evaluate the negative of the sum of evaluated numbers.
  • {A} - While 0 is not the top of the stack, do A. Then evaluate the sum of all runs in A before passing {A}.
  • <A> - Do A, but evaluate it as 0.

Phew, I explained how to Brain-Flak. Now for the numbers!

Numbers

  • Flak(1) = 1, evaluated from the code: ()
  • Flak(2) = 2, evaluated from the code: ()()
  • Flak(3) = 3, evaluated from the code: ()()()
  • Flak(4) = 4, evaluated from the code: ()()()()
  • Flak(5) = 6, evaluated from the code: (()()()){}
  • Flak(6) = 8, evaluated from the code: (()()()()){}
  • Flak(7) = 12, evaluated from the code: ((()()()){}){}
  • Flak(8) = 16, evaluated from the code: ((()()()()){}){}
  • Flak(9) = 24, evaluated from the code: (((()()()){}){}){}
  • Flak(10) = 32, evaluated from the code: (((()()()()){}){}){}
  • Flak(11) = 48, evaluated from the code: ((((()()()){}){}){}){}
  • Flak(12) = 64, evaluated from the code: ((((()()()()){}){}){}){}
  • Flak(13) = 96, evaluated from the code: (((((()()()){}){}){}){}){}
  • Flak(14) = 128, evaluated from the code: (((((()()()()){}){}){}){}){}
  • Flak(15) = 192, evaluated from the code: ((((((()()()){}){}){}){}){}){}
  • Flak(16) = 256, evaluated from the code: ((((((()()()()){}){}){}){}){}){}
  • Flak(17) = 384, evaluated from the code: (((((((()()()){}){}){}){}){}){}){}
  • Flak(18) = 512, evaluated from the code: (((((((()()()()){}){}){}){}){}){}){}
  • Flak(19) = 768, evaluated from the code: ((((((((()()()){}){}){}){}){}){}){}){}
  • Flak(20) = 2084, evaluated from the code: (((()()()()){})){({}<(({}){})>[()])}{}{}
  • Flak(21) = 49230, evaluated from the code: ((((()()()){}){})){({}<(({}){})>[()])}{}{}
  • Flak(22) = 1048712, evaluated from the code: ((((()()()()){}){})){({}<(({}){})>[()])}{}{}
  • Flak(23) = 402653484, evaluated from the code: (((((()()()){}){}){})){({}<(({}){})>[()])}{}{}
  • Flak(24) = 137438954000, evaluated from the code: (((((()()()()){}){}){})){({}<(({}){})>[()])}{}{}
  • Flak(25) = 13510798882112664, evaluated from the code: ((((((()()()){}){}){}){})){({}<(({}){})>[()])}{}{}
  • Flak(26) = 1180591620717411305504, evaluated from the code: ((((((()()()()){}){}){}){})){({}<(({}){})>[()])}{}{}
  • Flak(27) ~ f_3(3), evaluated from the code: ((()()())){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(28) ~ f_3(4), evaluated from the code: ((()()()())){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(29) ~ f_3(6), evaluated from the code: (((()()()){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(30) ~ f_3(8), evaluated from the code: (((()()()()){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(31) ~ f_3(12), evaluated from the code: ((((()()()){}){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(32) ~ f_3(16), evaluated from the code: ((((()()()()){}){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(33) ~ f_3(24), evaluated from the code: (((((()()()){}){}){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(34) ~ f_3(32), evaluated from the code: (((((()()()()){}){}){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(35) ~ f_3(48), evaluated from the code: ((((((()()()){}){}){}){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(36) ~ f_3(64), evaluated from the code: ((((((()()()()){}){}){}){})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}{}
  • Flak(37) ~ f_4(3), evaluated from the code: ((()()())){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(38) ~ f_4(4), evaluated from the code: ((()()()())){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(39) ~ f_4(6), evaluated from the code: (((()()()){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(40) ~ f_4(8), evaluated from the code: (((()()()()){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(41) ~ f_4(12), evaluated from the code: ((((()()()){}){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(42) ~ f_4(16), evaluated from the code: ((((()()()()){}){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(43) ~ f_4(24), evaluated from the code: (((((()()()){}){}){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(44) ~ f_4(32), evaluated from the code: (((((()()()()){}){}){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(45) ~ f_4(48), evaluated from the code: ((((((()()()){}){}){}){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(46) ~ f_4(64), evaluated from the code: ((((((()()()()){}){}){}){})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(47) ~ f_5(3), evaluated from the code: ((()()())){({}<(({})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(48) ~ f_5(4), evaluated from the code: ((()()()())){({}<(({})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(49) ~ f_5(6), evaluated from the code: (((()()()){})){({}<(({})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}>[()])}{}{}
  • Flak(50) ~ f_5(8), evaluated from the code: (((()()()()){})){({}<(({})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}>[()])}{}{}