A121305 -id:A121305 - cp's OEIS frontend

A036788 Length of Roman notation for n <= length of decimal representation.

1, 5, 10, 11, 15, 20, 40, 50, 51, 55, 60, 90, 100, 101, 102, 104, 105, 106, 109, 110, 111, 115, 120, 140, 150, 151, 155, 160, 190, 200, 201, 205, 210, 250, 300, 400, 401, 405, 410, 450, 500, 501, 502, 504, 505, 506, 509, 510, 511, 515, 520, 540, 550, 551, 555

Offset: 1

N. J. A. Sloane

The Roman numeration system used here is the naive one taught in primary school. This sequence, like many others involving numeration systems, is neither well-defined nor interesting for large values of n. - N. J. A. Sloane, Jul 03 2008

			15 = XV has length 2 in both notations.

Nathaniel Johnston, Table of n, a(n) for n = 1..199 (complete up to 3999)
Paul Lewis, Roman numerals

Cf. A036786, A036787, A105269, A119310, A121305.

a036788 n = a036788_list !! (n-1)
a036788_list = [x | x <- [1..], a006968 x <= a055642 x]
-- Reinhard Zumkeller, Apr 20 2013

for n from 1 to 3999 do if(length(convert(n, roman)) <= length(n))then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Select[Range[560],StringLength[IntegerString[#,"Roman"]]<= IntegerLength[ #]&] (* Harvey P. Dale, Dec 18 2011 *)

A006968(a(n)) <= A055642(a(n)). - Reinhard Zumkeller, Apr 20 2013

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Sep 25 2000

A002904 Delete all letters except c, d, i, l, m, v, x from the US English name of n, then read as Roman numeral if possible, otherwise 0.

Original entry on oeis.org

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, 9, 9, 9, 9, 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

Offset: 1

J. H. Conway

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

			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.)

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.

See A092302 and A121305 for other versions.

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)

a(35) and beyond from Michael S. Branicky, Jan 09 2023

cp's OEIS Frontend

A036788 Length of Roman notation for n <= length of decimal representation.

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