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%I #12 Aug 17 2022 22:29:46
%S 2,211,223,2003,2027,2203,2221,2000000000003,2000000000203,
%T 2000000002001,2000000002003,2000000002223,
%U 2000000000000000000000000000000000041,2000000000000000000000000000000000429,2000000000000000000000000000000000653
%N Each prime appears later in alphabetical order (in American English) than the one before.
%C From _Michael S. Branicky_, Aug 17 2022: (Start)
%C As in the companion sequence A050444, spaces, hypens and the word "and" are not included in the comparisons.
%C In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used.
%C The highest term is a(38) = 2*10^63 + 2*10^36 + 2*10^12 + 2202 ("two vigintillion two undecillion two trillion two thousand two hundred ninety three"). See b-file and link to US English names of terms. (End)
%H Michael S. Branicky, <a href="/A050445/b050445.txt">Table of n, a(n) for n = 1..38</a>
%H Michael S. Branicky, <a href="/A050445/a050445.txt">US English names of terms</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LargeNumber.html">Large Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Names_of_large_numbers">Names of Large Numbers</a>
%H Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_one">one hundred one</a> (US)
%H Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_and_one">one hundred and one</a> (UK)
%e Prime 2 ("two") is followed in alphabetic order first by prime 211 ("two hundred eleven").
%o (Python)
%o from sympy import isprime
%o from num2words import num2words
%o def n2w(n): return num2words(n).replace(" and", "").replace(chr(44), "").replace(chr(32), "").replace("-", "")
%o def afind(limit, start=2):
%o alst, last, t = [], start-1, start
%o while t <= limit:
%o target = n2w(last)
%o while not isprime(t) or n2w(t) <= target:
%o t += 1
%o if t > limit: return alst
%o last = t; alst.append(t)
%o return alst
%o print(afind(3000)) # _Michael S. Branicky_, Aug 17 2022
%Y Cf. A050444, A180301.
%K base,fini,full,nonn,word
%O 1,1
%A Michael Lugo (mlugo(AT)thelabelguy.com), Dec 23 1999
%E If you accept "vigintillion" as a name for 10^63 then there are more terms.
%E Offset changed, a(4) inserted and a(8) and beyond from _Michael S. Branicky_, Aug 17 2022
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