OFFSET
1,5
COMMENTS
From M. F. Hasler, Feb 21 2020: (Start)
There are several standards for Roman numerals, even though experts agree that none of them has ever been universally accepted, cf. references in Wikipedia article.
The current definition of the sequence uses "if possible", so whenever there is a possible interpretation according to any of these standards, it is acceptable.
Non-uniqueness could be caused by rare irregular variants which must be excluded in order to have a well-defined sequence. E.g., iixx will mean 18, not 22, although the standard notation for 18 is xviii (and xiix would also be used sometimes).
If required, the meaning of "possible" must be made more precise (e.g., allowing only "standard subtractive" or additionnally "standard additive" notation; this can be made completely explicit). (End)
There are 1411 nonzero terms; see Branicky link. - Michael S. Branicky, Jan 09 2023
The first term where British English differs from US is a(1001). This gives 500 in US English, but is invalid in British English (1001 is one thousanD anD one). - Paul Duckett, Oct 24 2024
LINKS
Michael S. Branicky, Table of n, a(n) for all nonzero a(n).
Brady Haran and N. J. A. Sloane, What Number Comes Next? (2018), Numberphile video.
Wikipedia, Roman numerals, as of Feb 19 2020.
FORMULA
From Michael S. Branicky, Jan 09 2023: (Start)
a(100..999) = 0, due to "dd".
a(k*1000) = 500 for k in {1..4, 10, 14, 20..24, 40..44};
a(k*1000+i) = (500 + a(i))*[a(i) != 0] for i in 1..99 for k in {1..4, 10, 14, 20..24, 40..44}; and
a(n) = 0 for all other 1100 <= n <= 999999, due to "id", "vd", "xd" or "dd".
a(n) = 0 for n >= 10^6, due to "ll".
(End)
EXAMPLE
To get a(5), write 5 = "five", delete 'f' & 'e' to get "iv", Roman for 4 = a(5).
To get a(35), write 35 = "thirty five", delete all but 'i's and 'v's, to get "iiv", which is not a legal Roman number*, so a(35) = 0 by definition of the sequence. (*It is never allowed to subtract more than one unit 'I' (or 'X' or 'C') from one of the symbols V, L, D representing 5 times a power of 10, as it is never allowed that one of V, L, D is subtracted from one of I, X, C, M.)
CROSSREFS
KEYWORD
nonn,word
AUTHOR
EXTENSIONS
a(35) and beyond from Michael S. Branicky, Jan 09 2023
STATUS
approved