A356024 a(n) is the next higher integer than n whose spelling in US English comes lexicographically later.

2, 200, 12, 6, 6, 10, 10, 9, 10, 12, 12, 20, 20, 16, 16, 20, 20, 19, 20, 21, 22, 200, 200, 26, 26, 200, 200, 29, 200, 31, 32, 200, 200, 36, 36, 200, 200, 39, 200, 41, 42, 60, 60, 46, 46, 60, 60, 49, 60, 51, 52, 60, 60, 56, 56, 60, 60, 59, 60, 61, 62, 200, 200

Offset: 1

Author

Michael S. Branicky, Jul 23 2022

Keywords

• nonn
• word

Comments

Alphabetical order is with commas removed, but with spaces included, e.g., 8800 ("eight thousand eight hundred") would precede 8018 ("eight thousand eighteen").

In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), is used.

Examples

			a(1) = 2 since "two" is after "one".
a(2) = 200 since "two hundred" is after "two".
a(2202) = 2000000000000 since "two trillion" is after "two thousand two hundred two".
		

Links

• Eric Weisstein's World of Mathematics, Large Number
• Wikipedia, Names of Large Numbers
• Wiktionary, one hundred one (US)
• Wiktionary, one hundred and one (UK)

Crossrefs

Cf. A180301.

Programs

Python

from num2words import num2words
def n2w(n): return num2words(n).replace(" and", "").replace(chr(44), "")
def a(n):
    target, t = n2w(n), n+1
    while n2w(t) <= target: t += 1
    return t
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Jul 23 2022

Formula

a(A180301(n)) = A180301(n+1).