A092320 "Word-factorable" numbers, or numbers k that are divisible by the number of letters in the American English word(s) for k.

4, 6, 12, 30, 33, 36, 40, 45, 50, 54, 56, 60, 70, 81, 88, 90, 100, 112, 150, 162, 170, 200, 240, 252, 300, 304, 336, 340, 405, 406, 418, 456, 513, 525, 528, 551, 560, 567, 600, 660, 665, 666, 693, 704, 720, 748, 810, 828, 850, 858, 874, 882, 897, 910, 924, 960, 1005

Offset

1,1

Comments

Cal Q. Leytor (obviously an alias) asked for the lowest pair of consecutive word-factorable numbers.

Lowest pair of consecutive word-factorable numbers is 405-406; next is 665-666. - Ray Chandler, Feb 16 2004

Subsequence of A002808 (composite numbers). - Ivan N. Ianakiev, Mar 01 2020

References

Cal Q. Leytor, The Word Factor, GAMES, October 1986, page 52.

Links

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

Example

"One hundred twelve" has 16 letters and 112=16*7, so 112 is a term.

Mathematica

Select[Range[1000], Divisible[#, StringLength[StringReplace[IntegerName[#],
{"\[Hyphen]" -> "", " " -> ""}]]] &] (* Ivan N. Ianakiev, Mar 01 2020 *)

Prog

(Python)
from num2words import num2words as n2w
def letters(n): return sum(c.isalpha() for c in n2w(n).replace(" and", ""))
def ok(n): return n%letters(n) == 0
print([k for k in range(1, 1000) if ok(k)]) # Michael S. Branicky, Jan 17 2022

Crossrefs

Sequence in context: A115076 A126259 A068570 * A056495 A351523 A263656

Adjacent sequences: A092317 A092318 A092319 * A092321 A092322 A092323

Keyword

easy,nonn,word

Author

Bryce Herdt (mathidentity(AT)aol.com), Feb 15 2004

Extensions

More terms from Ray Chandler, Feb 16 2004

Status

approved