A050445 Each prime appears later in alphabetical order (in American English) than the one before.

2, 211, 223, 2003, 2027, 2203, 2221, 2000000000003, 2000000000203, 2000000002001, 2000000002003, 2000000002223, 2000000000000000000000000000000000041, 2000000000000000000000000000000000429, 2000000000000000000000000000000000653

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

Cf. A050444, A180301.

Sequence in context: A178388 A056065 A317978 * A167833 A167838 A106100

Adjacent sequences: A050442 A050443 A050444 * A050446 A050447 A050448

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