A052362 Indices of records in length of English name of n including spaces and dashes (A052360): n such that k < n => A052360(k) < A052360(n).

0, 3, 11, 13, 17, 21, 23, 73, 101, 103, 111, 113, 117, 121, 123, 173, 323, 373, 1101, 1103, 1111, 1113, 1117, 1121, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 21373, 23323, 23373, 73373, 101323, 101373, 103323, 103373, 111373, 113323, 113373, 117373

Offset: 1

Author

Allan C. Wechsler, Mar 07 2000

Keywords

• nonn
• word
• nice
• easy

Comments

From M. F. Hasler, Aug 12 2020: (Start)

This sequence uses A052360 which counts all characters in the English name of the numbers, including spaces and hyphens, in contrast to A052363 which uses A005589 which only counts the letters. Thus, e.g., "twenty-one" is in this sequence but not in A052363.

It appears that from 1323 on, all terms end in -323 or in -373. After 117(373) these are prefixed by 121, 123, 173, 323, 373 (thousand). Then the next terms is 1'103'323, and after 1'373'373, the next terms are > 3*10^6, then > 11*10^6, etc.

I conjecture that from 103 on all d-digit terms have a smaller (most often but not always (d-1)-digit) term as suffix, and from 173 on they also have an earlier term as prefix. (End)

Examples

			From _M. F. Hasler_, Aug 12 2020: (Start)
The first term is zero, since all other nonnegative integers (thus certainly all those with longer names) are larger than zero.
"One" and "two" are not in the sequence, since "zero" is smaller but has a longer name.
"Three" is again in the sequence since all smaller numbers (0, 1 and 2) have shorter names. And so on. (End)
		

Crossrefs

Cf. A005589, A052360, A052363.

Programs

PARI

m=0;for(n=0,2e5, if(m<A052360(n), m=A052360(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 len(n2w(n).replace(" and", "").replace(chr(44), ""))
def agen():
    record = 0
    for n in count(0):
        value = f(n)
        if value > record: yield n; record = value
print(list(islice(agen(), 46))) # Michael S. Branicky, Jul 12 2022

Extensions

Minor edits by Ray Chandler, Jul 22 2009

Name and example edited and more terms by M. F. Hasler, Aug 12 2020