So a few days ago, I was talking with Boris at the Discord Googology Server. He explained to me a function that he had made, but he didn't know how to define it. So in this blog post, i will define that function, which for now I'll call it as Boboris02's Modular Function.

First, remember this table for converting digits to letters. It will be important.

Digit | Letter |
---|---|

0 | Remove it |

1 | A |

2 | B |

3 | C |

4 | D |

5 | E |

6 | F |

7 | G |

8 | H |

9 | I |

Now, we need to define what a letter code is.

A letter code (represented with C or C_{n}) is a string that is made up of letters (X does not count as a letter in a letter code) and K_{n}.

And now, we define some functions.

## C(n) function

C(n) accepts either a string of only letters or a string of only numbers as it's input. If the input is a string of digits, it will convert each of them into a letter. If the input is a string of letters, it will convert each of them into a digit. It uses the table above to convert digits to letters and letters to digits.

Examples: C(4) = D, C(EIH) = 598, C(0) = blank (the 0 was removed)

## R(a,b) function

R(a,b) only accepts a number for both of its inputs. It generates a letter code out of the 2 inputs.

To calculate R(a,1), calculate C(a), then if a is prime, add XK_{n} at the start, else, add K_{n} at the start (n is the number of digits of a)

To calculate R(a,b) (b>1), first calculate R(a,b-1), then convert every L (L represents a letter) in R(a,b-1) to R(C(L),1)

Examples: R(5,1) = XK_{1}E, R(5,2) = XK_{1}XK_{1}E.

## S(a,b) function

WIP