OFFSET
0,6
COMMENTS
Not well-defined! A002904 is the main entry for this sequence. - N. J. A. Sloane, Sep 28 2011.
There are a finite number of nonzero values because "hunDreD" and "mILLIon" and "bILLIon" and "trILLIon" and so forth yield non-well-formed Roman numerals. The largest n such that a(n) is nonzero is 94044 maps to "nInetyfour thousanD fortyfour" maps to "ID" maps to 499.
Allowing a(94044) = 499 because of "ID" speaks to the non-standard usage (499 = "CDXCIX") that makes this sequence, as mentioned above, not necessarily well-defined. If "ID" is ok, why not "IIV" for a(35)? If we take Mathematica's RomanNumeral conversion as standard (for integers 1-4999; starting with 5000 we generate overbars), then there are 1411 nonzero entries up to and including a(44099) = 502. Specifically, I (30 solutions), II (8), IV (7), V (9), VI (2), IX (9), LV (2), D (272), DI (480), DII (128), DIV (112), DV (144), DVI (32), DIX (144), and DLV (32). - Hans Havermann, May 06 2019
LINKS
Brady Haran and N. J. A. Sloane, What Number Comes Next? (2018), Numberphile video
FORMULA
Take English name of n as string of characters, eliminate all spaces, hyphens and letters other than I, V, X, L, C, D, M. Interpret remaining string as a Roman numeral, assigning 0 if the string is not well-formed and a(n) is well-formed.
EXAMPLE
a(5) = 4 because 5 maps to "five" maps to "fIVe" maps to "IV" maps to 4.
a(6) = 9 because 6 maps to "six" maps to "sIX" maps to "IX" maps to 9.
a(7) = 5 because 7 maps to "seven" maps to "seVen" maps to "V" maps to 5.
a(8) = 1 because 8 maps to "eight" maps to "eIght" maps to "I" maps to 1.
a(9) = 1 because 9 maps to "nine" maps to "nIne" maps to "I" maps to 1.
a(35) = 0 because 35 maps to "thirty-five" maps to "thIrty-fIVe" maps to "IIV" which is not a well-formed Roman nhumeral, hence maps to 0.
a(1000) = 500 because 1000 maps to "one thousand" maps to "one thousanD" maps to "D" maps to 500.
CROSSREFS
KEYWORD
base,easy,nonn,word
AUTHOR
Jonathan Vos Post, Sep 05 2006
STATUS
approved