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 A121305 Value of Roman numeral embedded in English name of n, or 0 if no such value exists. 2
 0, 0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1, 9, 5, 1, 1, 0, 0, 0, 0, 0, 4, 9, 5, 1, 1, 1, 1, 1, 1, 1, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 4, 9, 5, 1, 1, 1, 1, 1, 1, 1, 0, 0, 4, 2, 2, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0, 0, 6, 6, 1, 1, 1, 1, 1, 0, 0, 4, 2, 2, 1, 1, 1, 1, 1, 0, 0, 4, 2, 2, 0 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A002904, A005589. Sequence in context: A200629 A021206 A002904 * A200396 A011513 A164818 Adjacent sequences:  A121302 A121303 A121304 * A121306 A121307 A121308 KEYWORD base,easy,nonn,word AUTHOR Jonathan Vos Post, Sep 05 2006 STATUS approved

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Last modified February 20 08:03 EST 2020. Contains 332069 sequences. (Running on oeis4.)