OFFSET
1,1
COMMENTS
From Michael S. Branicky, Aug 17 2022: (Start)
As in the companion sequence A050444, spaces, hypens and the word "and" are not included in the comparisons.
In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used.
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)
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..38
Michael S. Branicky, US English names of 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)
EXAMPLE
Prime 2 ("two") is followed in alphabetic order first by prime 211 ("two hundred eleven").
PROG
(Python)
from sympy import isprime
from num2words import num2words
def n2w(n): return num2words(n).replace(" and", "").replace(chr(44), "").replace(chr(32), "").replace("-", "")
def afind(limit, start=2):
alst, last, t = [], start-1, start
while t <= limit:
target = n2w(last)
while not isprime(t) or n2w(t) <= target:
t += 1
if t > limit: return alst
last = t; alst.append(t)
return alst
print(afind(3000)) # Michael S. Branicky, Aug 17 2022
CROSSREFS
KEYWORD
base,fini,full,nonn,word
AUTHOR
Michael Lugo (mlugo(AT)thelabelguy.com), Dec 23 1999
EXTENSIONS
If you accept "vigintillion" as a name for 10^63 then there are more terms.
Offset changed, a(4) inserted and a(8) and beyond from Michael S. Branicky, Aug 17 2022
STATUS
approved