A213006 Positive numbers that, spelled in English, are as long as the spelling of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 18, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 3010, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 4010, 5001, 5002, 5003, 5004, 5005, 5006, 5007, 5008, 5009, 5010, 6001, 6002, 6003

Offset

1,2

Comments

Dan Hoey came up with an inequality Spell_Length(n)<=A*n+B (I've forgotten A and B, which are fairly small rationals: equality at two points), that was used to limit the maximum length of a self-enumerating sentence, and thus make an exhaustive search possible. - R. H. Hardin, Feb 22 2012

References

Eric Angelini, Posting to Sequence Fans Mailing List, Feb 12 2012

Hans Havermann, Posting to Sequence Fans Mailing List, Feb 23 2012

Links

Hans Havermann, Table of n, a(n) for n = 1..10000

Example

11 = eleven (6 letters) = one one (6 letters)
1002 = one thousand two (14 letters) = one zero zero two (14 letters).

Prog

(Python)
from num2words import num2words as n2w
m = {"0":4, "1":3, "2":3, "3":5, "4":4, "5":4, "6":3, "7":5, "8":5, "9":4}
def dl(n): return sum(m[d] for d in str(n))
def wl(n): return sum(1 for c in n2w(n).replace(" and", "") if c.isalpha())
def ok(n): return dl(n) == wl(n)
print([k for k in range(1, 7000) if ok(k)]) # Michael S. Branicky, Apr 03 2023

Crossrefs

Sequence in context: A037173 A091897 A055201 * A068998 A072303 A242413

Adjacent sequences: A213003 A213004 A213005 * A213007 A213008 A213009

Keyword

nonn,base,word

Author

N. J. A. Sloane, Jun 01 2012

Status

approved