20

# Challenge description

We've had a few challenges involving the Look-and-say sequence. Quick reminder:

- The sequence starts with
`1`

, - Subsequent terms of this sequence are generated by enumerating each group of repeating digits in the previous term,

So the first few terms are:

```
1 "one"
11 "one one" (we look at the previous term)
21 "two ones"
1211 "one two, one one"
111221 "one one, one two, two ones"
312211 "three ones, two twos, one one"
```

Now let's do the same thing, but use Roman Numerals instead. We start with `I`

and follow the same rules (we apply the digit-counting rule to characters instead, so we read `IVX`

as `one one, one five, one ten`

instead of `one four, one ten`

or some other way):

```
I "one"
II "one one"
III "two ones" = "II" + "I"
IIII "three ones" = "III" + "I"
IVI "four ones" = "IV" + "I"
IIIVII "one one, one five, one one"
IIIIIVIII "three ones, one five, two ones" = ("III" + "I") + ("I" + "V") + ("II" + "I")
```

Given a positive integer `N`

, either:

- Output first
`N`

numerals of this sequence (any reasonable separator is fine, as well as`["I", "II", "III", ...]`

- Output
`N`

th term of this sequence (it may be 0-indexed).

Remember to make your code as short as possible, since this is a code-golf challenge!

EDIT: I believe that there is always one standard/preferred way of expressing integers as roman numerals, (like `95`

-> `XCV`

instead of `VC`

). Couple of Roman numeral converters I found online corroborate my opinion. If in doubt, use an online converter, as listing all the possible edge-cases and specific rules of writing Roman numerals is not the point of this challenge.

EDIT2: @PeterTaylor and @GregMartin pointed out that only numbers less or equal to `5`

appear in the sequence, so you don't have to worry about the ambiguity of Roman numerals (numbers `1`

- `8`

are `I`

, `II`

, `III`

, `IV`

, `V`

, `VI`

, `VII`

, and `VIII`

)

There isn't a unique Roman numeral expression for each integer. Which numbers might it be necessary to express, and which expressions of those numbers are valid? – Peter Taylor – 2016-08-30T15:13:47.410

What do you mean by "there isn't a unique Roman numeral expression for each integer"? Like

`4`

/`IV`

/`IIII`

? Or`95`

/`XCV`

/`VC`

? There might not always be a unique way to express an integer, but I'm pretty sure there's always a preferred (standard) one - correct me if I'm wrong. – shooqie – 2016-08-30T15:17:52.8131how far do we have to go with our roman numberals? – Maltysen – 2016-08-30T15:19:30.157

Yes, both of those cases. In the second case, I think it's very much a matter of opinion which is preferable. – Peter Taylor – 2016-08-30T15:21:59.777

@Maltysen I think the number of equal digits that can appear in succession is limited to 7. – Martin Ender – 2016-08-30T15:22:21.457

@shooqie I agree with you on this one, but you might just want to solidify the rules for roman numerals in OP. – Maltysen – 2016-08-30T15:26:17.573

@Maltysen: Like, this is something that bothers me the most about this site. Make a challenge a tiny bit more complicated and you get questions like

`what counts as X?`

or`what about the edge-case #98752314?`

– shooqie – 2016-08-30T15:35:35.4609@shooqie if these details weren't clarified, how would you compare answers? If there are certain edge cases left up to interpretation the actual scores become meaningless because they might make a bigger difference than any golfing tricks you could come up with. – Martin Ender – 2016-08-30T16:41:14.420

@MartinEnder: Well, I did my best at clearing up the confusion about the Roman numerals, but I feel like I shouldn't have to say how to write them - we've had challenges with Roman numerals before and there didn't seem to be any confusion whatsoever. – shooqie – 2016-08-30T17:00:28.490

I don't understand the output format - are we converting to roman numerals, grouping by character type, counting the length of each group and turning the whole thing into roman numerals again? – Blue – 2016-08-30T17:30:15.797

@muddyfish: Yeah, pretty much. – shooqie – 2016-08-30T17:32:30.953

I think one can mathematically prove that numbers greater than 8 never appear in the sequence starting at

`I`

. If so, then programs need only consider`I`

s and`V`

s. – Greg Martin – 2016-08-30T18:46:46.700@GregMartin, it's possible to prove the stronger statement that no run-length greater than 5 appears in the sequence whose first generation is

`I`

. – Peter Taylor – 2016-08-30T21:56:00.0331k rep! Congrats :) – ThreeFx – 2016-08-30T23:51:18.757

@GregMartin: Well, that certainly makes things easier. – shooqie – 2016-08-31T07:57:21.007

Surprisingly roman numerals are in fact a decimal notation where a number is split into powers of 10. So

`999`

=`900+90+9`

=`CM + XC + IX`

=`CMXCIX`

and not`IM`

(This is the modern standard form. The romans themselves were not completely consistent). But as noted this is not needed here. – Ton Hospel – 2016-09-01T06:02:06.530