A036786 Length of Roman notation for n < length of decimal representation.

10, 50, 100, 101, 105, 110, 150, 200, 400, 500, 501, 505, 510, 550, 600, 900, 1000, 1001, 1002, 1004, 1005, 1006, 1009, 1010, 1011, 1015, 1020, 1040, 1050, 1051, 1055, 1060, 1090, 1100, 1101, 1105, 1110, 1150, 1200, 1400, 1500, 1501, 1505, 1510, 1550

Offset: 1

Author

J. H. Conway

Keywords

• nonn
• nice
• easy
• base

Examples

			1000 = M is shorter in Roman numerals, so 1000 is in this sequence.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..55 (complete up to 3999)

Crossrefs

Cf. A036787, A036788.

Programs

Haskell

a036786 n = a036786_list !! (n-1)
a036786_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[2000],StringLength[IntegerString[#,"Roman"]]Harvey P. Dale, Feb 10 2015 *)

Formula

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

Extensions

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