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

1,2

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

Links

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

Paul Lewis, Roman numerals

Formula

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

Example

15 = XV has length 2 in both notations.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A136823 A275200 A225838 * A351327 A136811 A130228

Adjacent sequences: A036785 A036786 A036787 * A036789 A036790 A036791

Keyword

nonn,base,easy,nice

Author

N. J. A. Sloane

Extensions

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

Status

approved