What is the smallest number which, when expressed in Roman numerals, won't fit in a 280-character Tweet?

high-water-mark-roman.js

// <https://twitter.com/Revolvolutionry/status/1165616879009816576>
// <https://oeis.org/A036746>

const { arabicToRoman, romanToArabic } = require('big-roman')

// The entry at index `i` in this array is the smallest Roman numeral
// of length `i`
const results = ['']
const stopAt = 281
let powerOfTen = 0
while (results.length < stopAt) {
	// Batch up the new watermarks on a per-new-digit basis, otherwise we end
	// up accidentally trying to e.g. combine new Roman digit 'IV' with
	// existing high water mark 'II' and then incorrectly noting down 'IVII' as
	// the smallest Roman numeral of length 4
	const batch = {}

	for (let value = 0; value < 10; value++) {
		const romanDigit = arabicToRoman(String(value) + '0'.repeat(powerOfTen))
		results.forEach(result => {
			const newRomanNumeral = romanDigit + result
			const newLength = newRomanNumeral.length
			if (!(newLength in results) && !(newLength in batch)) {
				batch[newLength] = newRomanNumeral
			}
		})
	}

	for (const newLength in batch) {
		results[newLength] = batch[newLength]
	}

	powerOfTen++
}

results.forEach((result, i) => {
	console.log(i, result, result === '' ? '0' : romanToArabic(result))
})

const answer = results[stopAt]

console.log(`First Roman numeral which won't fit in a Tweet: ${answer} = ${romanToArabic(answer)}`)

The first Roman numeral which won't fit in a Tweet is X̅̅̅̅̅̅X̅̅̅̅̅̅X̅̅̅̅̅̅V̅̅̅̅̅̅M̅̅̅̅̅M̅̅̅̅̅M̅̅̅̅̅D̅̅̅̅̅C̅̅̅̅̅C̅̅̅̅̅C̅̅̅̅̅L̅̅̅̅̅X̅̅̅̅̅X̅̅̅̅̅X̅̅̅̅̅V̅̅̅̅̅M̅̅̅̅M̅̅̅̅M̅̅̅̅D̅̅̅̅C̅̅̅̅C̅̅̅̅C̅̅̅̅L̅̅̅̅X̅̅̅̅X̅̅̅̅X̅̅̅̅V̅̅̅̅M̅̅̅M̅̅̅M̅̅̅D̅̅̅C̅̅̅C̅̅̅C̅̅̅L̅̅̅X̅̅̅X̅̅̅X̅̅̅V̅̅̅M̅̅M̅̅M̅̅D̅̅C̅̅C̅̅C̅̅L̅̅X̅̅X̅̅X̅̅V̅̅M̅M̅D̅C̅C̅C̅L̅X̅X̅X̅V̅MMMDCCCLXXXVIII = 38,888,888,888,887,888,888.

I used big-roman to work this out.