0,6

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.

5.

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.

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.

Cf. A005589.

Cf. A002904. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2008]

Sequence in context: A087369 A021206 A002904 this_sequence A011513 A164818 A065796

Adjacent sequences: A121302 A121303 A121304 this_sequence A121306 A121307 A121308

base,easy,nonn,word

Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 05 2006