Playing with Roman numerals

What is the longest year number (yet) written in Roman numerals?

library(tidyverse)

tibble(y = 1:2020) |>
  mutate(r = as.roman(y),
         l = str_length(r)) |>
  slice_max(l)

# A tibble: 1 × 3
      y r                 l
  <int> <roman>       <int>
1  1888 MDCCCLXXXVIII    13

It is year 1888, with 13 characters…

And the largest writable number being 3899, according to the strict rules in R (however some say it’s 3999),

tibble(y = 1:5000) |>
  mutate(r = as.roman(y),
         l = str_length(r)) |>
  filter(lead(is.na(l))) |> 
  slice_min(l)

# A tibble: 1 × 3
      y r               l
  <int> <roman>     <int>
1  3899 MMMDCCCXCIX    11

the longest overall year will be year 3888 with 15 characters.

tibble(y = 1:3899) |>
  mutate(r = as.roman(y),
         l = str_length(r)) |>
  slice_max(l)

# A tibble: 1 × 3
      y r                   l
  <int> <roman>         <int>
1  3888 MMMDCCCLXXXVIII    15

Nice pattern:

tibble(y = 1:3899) |>
  mutate(r = as.roman(y),
         l = str_length(r)) |>
  ggplot(aes(y, l)) +
  geom_point(alpha = .2) +
  geom_smooth() +
  labs(title = "Characters length of roman numeral years",
     x = "year",
     y = "characters")

And there are only eleven palindromic years:

tibble(y = 1:3899) |>
  mutate(r = as.character(as.roman(y)),
         rr = stringi::stri_reverse(r)) |> 
  filter(r == rr,
         str_length(r) > 1)

# A tibble: 11 × 3
       y r     rr   
   <int> <chr> <chr>
 1     2 II    II   
 2     3 III   III  
 3    19 XIX   XIX  
 4    20 XX    XX   
 5    30 XXX   XXX  
 6   190 CXC   CXC  
 7   200 CC    CC   
 8   300 CCC   CCC  
 9  1900 MCM   MCM  
10  2000 MM    MM   
11  3000 MMM   MMM