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 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!
- 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: (((()()()()){})){({}<(({})){({}<(({})){({}<(({})){({}<(({}){})>[()])}{}>[()])}{}>[()])}{}>[()])}{}{}