A108017 Position of integer n in the list of first n natural numbers written out in English (without "and") and arranged in alphabetical order.

1, 2, 2, 1, 1, 4, 4, 1, 4, 8, 2, 11, 10, 5, 3, 11, 10, 2, 9, 19, 20, 21, 21, 20, 20, 23, 23, 20, 23, 17, 18, 19, 19, 18, 18, 21, 21, 18, 21, 6, 7, 8, 8, 7, 7, 10, 10, 7, 10, 5, 6, 7, 7, 6, 6, 9, 9, 6, 9, 35, 36, 37, 37, 36, 36, 39, 39, 36, 39, 33, 34, 35, 35, 34, 34, 37, 37, 34, 37, 3, 4, 5, 5

Offset

1,2

Comments

In going to higher terms, we use the conventions in A005589: spaces, hyphens and commas are removed before sorting. Thus, a(800) = 3 from EIGHT, EIGHTEEN, EIGHTHUNDRED, ..., not 2 from EIGHT, EIGHT HUNDRED, EIGHTEEN, ... . - Michael S. Branicky, Dec 28 2025

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(19) = 9 because of the ordered list: EIGHT, EIGHTEEN, ELEVEN, FIFTEEN, FIVE, FOUR, FOURTEEN, NINE, NINETEEN, ..., TWELVE, TWO.
a(21) = 20 because of the ordered list: EIGHT, ..., TWENTY, TWENTYONE, TWO.

Prog

(Python)
from num2words import num2words
from bisect import bisect, insort
from itertools import count, islice
def agen(): # generator of terms
    s = [""]
    for n in count(1):
        sn = "".join(c for c in num2words(n).replace(" and", "") if c.isalpha())
        an = bisect(s, sn)
        insort(s, sn)
        yield an
print(list(islice(agen(), 83))) # Michael S. Branicky, Dec 28 2025

Crossrefs

Cf. A005589, A214095 (in French).

Sequence in context: A053390 A140643 A331409 * A293208 A247364 A301895

Adjacent sequences: A108014 A108015 A108016 * A108018 A108019 A108020

Keyword

nonn,word

Author

Lekraj Beedassy, May 31 2005

Extensions

a(21) onward corrected by Michael S. Branicky, Dec 28 2025

Status

approved