OFFSET
1,1
COMMENTS
After a(7), the sequence contains only terms of the form a(i) * 10^(3*k) and a(i) * 10^(3*k) + a(j) for 1 <= i, j <= 7, where the name of 10^(3*k) is useless, e.g., 10^6 (million), 10^9 (billion), 10^12 (trillion), 10^27 (octillion), 10^30 (nonillion), ... (see links for large number names). - Michael S. Branicky, Jan 01 2021
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000
Michael Joseph Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002).
Eric Weisstein's World of Mathematics, Large Number
Wikipedia, Names of Large Numbers
EXAMPLE
30 is a term since its name THIRTY has no E, S or U.
PROG
(Python)
from num2words import num2words
from itertools import islice, product
def ok(n): return set(num2words(n).replace(" and", "")) & set("use") == set()
def agen(): # generator of terms < 10**304
base, pows = [k for k in range(1, 1000) if ok(k)], [1]
yield from ([0] if ok(0) else []) + base
for e in range(3, 304, 3):
if set(num2words(10**e)[4:]) & set("use") == set():
pows = [10**e] + pows
for t in product([0] + base, repeat=len(pows)):
if t[0] == 0: continue
yield sum(t[i]*pows[i] for i in range(len(t)))
print(list(islice(agen(), 31))) # Michael S. Branicky, Jan 15 2026
CROSSREFS
KEYWORD
nonn,word
AUTHOR
Michael Joseph Halm, Aug 23 2002
EXTENSIONS
Removed 'ninety' and 'ninety two' from the sequence which clearly include the letter E. Likewise removed 'two hundrEd' and others. Inserted 'thirty' and 'thirty-two'. - Freddie Noble, Jan 01 2021
a(16)-a(31) from Michael S. Branicky, Jan 01 2021
STATUS
approved