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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Comments

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

Examples

			15 = XV has length 2 in both notations.
		

Links

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

Crossrefs

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

Programs

Haskell

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

Maple

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

Mathematica

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

Formula

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

Extensions

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