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
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