A345015 Starting with 1, the next entry is the next higher odd integer whose spelling in English comes lexicographically earlier.

1, 5, 11, 81, 85, 801, 805, 811, 881, 885, 808001, 808005, 808011, 808081, 808085, 808801, 808805, 808811, 808881, 808885, 808000001, 808000005, 808000011, 808000081, 808000085, 808000801, 808000805, 808000811, 808000881, 808000885, 808808001, 808808005

Offset

1,2

Comments

From Michael S. Branicky, Jan 04 2022: (Start)

The restriction to odd numbers prevents the trivial sequence 1, 4, 5, 8 noted in A180301.

US English is used, so 101 is "one hundred one".

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

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

a(41) = 8000000001 ("eight billion one"). The highest term is a(80) = 8*10^9 + a(40) = 8808808885 ("eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-five"). See link to US English names of terms. (End)

Links

Michael S. Branicky, Table of n, a(n) for n = 1..80

Michael S. Branicky, US English names of all terms

Eric Weisstein's World of Mathematics, Large Number

Wikipedia, Names of Large Numbers

Wiktionary, one hundred one (US)

Wiktionary, one hundred and one (UK)

Formula

From Michael S. Branicky, Jan 04 2022: (Start)

a(10+i) = 808000 + a(i), for i in 1..10.

a(20+i) = 808000000 + a(i), for i in 1..20.

a(40+i) = 8000000000 + a(i), for i in 1..40. (End)

Example

The first term 1 ("one") is preceded in lexicographic order first by odd number 5 ("five"), which is preceded by odd number 11 ("eleven"), and so on.

Mathematica

list = {1};
Do [ If  [ -1 ==
    AlphabeticOrder [   IntegerName [ list[[-1]] , "Words"] ,
     IntegerName [ i, "Words" ] ], AppendTo [ list, i] ], {i, 1, 10^5,
    2}];
list

Prog

(Python)
from num2words import num2words
def n2w(n):
    return num2words(n).replace(" and", "") .replace(", ", "")
def afind(startfrom=1, limit=float('inf')):
    last, t = startfrom, startfrom + 1 + startfrom%2
    if startfrom%2 == 1:
        print(startfrom, end=", ")
    while t <= limit:
        target = n2w(last)
        while n2w(t) >= target:
            t += 2
            if t > limit: return
        last = t
        print(t, end=", ")
afind(limit=10**6) # Michael S. Branicky, Jan 04 2022

Crossrefs

Cf. A180301.

Sequence in context: A154797 A161852 A319537 * A002359 A292754 A090518

Adjacent sequences: A345012 A345013 A345014 * A345016 A345017 A345018

Keyword

nonn,word,fini,full

Author

Paul Erickson, Sep 15 2021

Extensions

a(11) and beyond from Michael S. Branicky, Jan 04 2022

Status

approved