

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
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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 selfenumerating 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)


CROSSREFS



KEYWORD

nonn,base,word


AUTHOR



STATUS

approved



