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A213006 Positive numbers that, spelled in English, are as long as the spelling of their digits. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,base,word
AUTHOR
N. J. A. Sloane, Jun 01 2012
STATUS
approved

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Last modified April 23 23:26 EDT 2024. Contains 371917 sequences. (Running on oeis4.)