A384131 Smallest positive number divisible by n that has n letters in US English, or 0 if none exists.

6, 4, 40, 12, 70, 56, 36, 100, 33, 300, 1000000001, 406, 150, 112, 170, 162, 418, 11020, 336, 528, 828, 4800, 3300, 1404, 1620, 1512, 1218, 1770, 1147, 1344, 1353, 2788, 3325, 3888, 12728, 13376, 13338, 103360, 22878, 23478, 27778, 101728, 103725, 111734, 111578

Offset

3,1

Comments

The GCHQ reference uses British English (including "and"). The disagreements are at a(14)-a(16), which the book lists as 70000000, 15000, 14000. Furthermore, the book lists a(13) as impossible.

References

GCHQ, The GCHQ Puzzle Book, Penguin, 2016 (see p. 47).

Links

Michael S. Branicky, Table of n, a(n) for n = 3..100 (terms 3..69 from Jason Bard)

Formula

a(n) >= A134629(n). - Michael S. Branicky, May 21 2025

Mathematica

mmax = 10^10; Do[m = n; While[StringLength[StringDelete[IntegerName[m, "Words"], {" ", "-", "\[Hyphen]", ", "}]] != n, m += n; If[m > mmax, m = 0; Break[]]]; Print[m], {n, 3, 43}]

Prog

(Python)
from num2words import num2words
from itertools import count, islice
def b(n): return sum(1 for c in num2words(n).replace(" and", "") if c.isalpha())
def a(n): return next(k for k in count(n, n) if b(k) == n)
print([a(n) for n in range(3, 13)]) # Michael S. Branicky, May 20 2025

Crossrefs

Cf. A005589, A134629.

Sequence in context: A038258 A298776 A114330 * A098657 A126936 A333813

Adjacent sequences: A384128 A384129 A384130 * A384132 A384133 A384134

Keyword

nonn,word

Author

Jason Bard, May 20 2025

Status

approved