A052363 Numbers n whose English name has a greater length (A005589) than any smaller number.

0, 3, 11, 13, 17, 23, 73, 101, 103, 111, 113, 117, 123, 173, 323, 373, 1103, 1111, 1113, 1117, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323, 103373, 111373, 113323, 113373, 117373, 123323, 123373, 173373, 323373, 373373

Offset: 1

Author

Allan C. Wechsler, Mar 07 2000

Keywords

• nonn
• word

Comments

Indices of records in A005589 (which only counts letters, but not spaces and punctuation, in the English name of numbers).

Examples

			Note that A052360(373373) = 64 and A005589(373373) = 56.
Sequence A052362 uses A052360 which also counts spaces and dashes, therefore "twenty-one" is in that sequence but not in this one: it uses one more character ('-') but has the same number of letters than "seventeen". - _M. F. Hasler_, Aug 12 2020
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..597 (terms < 10^54)
• Eric Weisstein's World of Mathematics, Number
• Eric Weisstein's World of Mathematics, Large Number
• Wikipedia, Names of Large Numbers
• Wiktionary, one hundred one (US)
• Wiktionary, one hundred and one (UK)
• Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens

Crossrefs

Cf. A005589, A052360, A052362.

Programs

PARI

m=0; for(n=0, 2e6, if(m<A005589(n), m=A005589(n); print1(n", "))) \\ M. F. Hasler, Aug 12 2020

Python

from itertools import count, islice
from num2words import num2words as n2w
def f(n): return sum(1 for c in n2w(n).replace(" and", "") if c.isalpha())
def agen():
    record = 0
    for n in count(0):
        value = f(n)
        if value > record: yield n; record = value
        n += 1
print(list(islice(agen(), 40))) # Michael S. Branicky, Jul 12 2022

Extensions

Edited by R. J. Mathar and T. D. Noe, Apr 09 2009

Minor edits by Ray Chandler, Jul 22 2009

a(41) and beyond from Michael S. Branicky, Jul 12 2022