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

%I A345015 #19 Feb 16 2025 22:38:59
%S A345015 1,5,11,81,85,801,805,811,881,885,808001,808005,808011,808081,808085,
%T A345015 808801,808805,808811,808881,808885,808000001,808000005,808000011,
%U A345015 808000081,808000085,808000801,808000805,808000811,808000881,808000885,808808001,808808005
%N A345015 Starting with 1, the next entry is the next higher odd integer whose spelling in English comes lexicographically earlier.
%C A345015 From _Michael S. Branicky_, Jan 04 2022: (Start)
%C A345015 The restriction to odd numbers prevents the trivial sequence 1, 4, 5, 8 noted in A180301.
%C A345015 US English is used, so 101 is "one hundred one".
%C A345015 Alphabetical order is with commas removed, but with spaces and hyphens included, e.g., 8800 ("eight thousand eight hundred") precedes 8018 ("eight thousand eighteen").
%C A345015 In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used.
%C A345015 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)
%H A345015 Michael S. Branicky, <a href="/A345015/b345015.txt">Table of n, a(n) for n = 1..80</a>
%H A345015 Michael S. Branicky, <a href="/A345015/a345015.txt">US English names of all terms</a>
%H A345015 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LargeNumber.html">Large Number</a>
%H A345015 Wikipedia, <a href="https://en.wikipedia.org/wiki/Names_of_large_numbers">Names of Large Numbers</a>
%H A345015 Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_one">one hundred one</a> (US)
%H A345015 Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_and_one">one hundred and one</a> (UK)
%F A345015 From _Michael S. Branicky_, Jan 04 2022: (Start)
%F A345015 a(10+i) = 808000 + a(i), for i in 1..10.
%F A345015 a(20+i) = 808000000 + a(i), for i in 1..20.
%F A345015 a(40+i) = 8000000000 + a(i), for i in 1..40. (End)
%e A345015 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.
%t A345015 list = {1};
%t A345015 Do [ If  [ -1 ==
%t A345015     AlphabeticOrder [   IntegerName [ list[[-1]] , "Words"] ,
%t A345015      IntegerName [ i, "Words" ] ], AppendTo [ list, i] ], {i, 1, 10^5,
%t A345015     2}];
%t A345015 list
%o A345015 (Python)
%o A345015 from num2words import num2words
%o A345015 def n2w(n):
%o A345015     return num2words(n).replace(" and", "") .replace(chr(44), "")
%o A345015 def afind(startfrom=1, limit=float('inf')):
%o A345015     last, t = startfrom, startfrom + 1 + startfrom%2
%o A345015     if startfrom%2 == 1:
%o A345015         print(startfrom, end=", ")
%o A345015     while t <= limit:
%o A345015         target = n2w(last)
%o A345015         while n2w(t) >= target:
%o A345015             t += 2
%o A345015             if t > limit: return
%o A345015         last = t
%o A345015         print(t, end=", ")
%o A345015 afind(limit=10**6) # _Michael S. Branicky_, Jan 04 2022
%Y A345015 Cf. A180301.
%K A345015 nonn,word,fini,full
%O A345015 1,2
%A A345015 _Paul Erickson_, Sep 15 2021
%E A345015 a(11) and beyond from _Michael S. Branicky_, Jan 04 2022