A160676 Numbers k such that k and 2k use the same number of characters when expressed in Roman numerals.

2, 5, 7, 13, 18, 20, 22, 31, 36, 46, 50, 52, 55, 57, 63, 68, 70, 72, 81, 86, 95, 97, 103, 108, 123, 126, 130, 132, 135, 137, 145, 147, 153, 158, 173, 176, 180, 182, 185, 187, 198, 200, 202, 205, 207, 213, 218, 220, 222, 231, 236, 246, 254, 261, 266, 274

Offset: 1

Author

Claudio Meller, May 23 2009

Keywords

• nonn
• easy
• base

Comments

Example: 2 and its double 4 both need two characters in Roman numerals: 2=II, 4=IV. Also 5=V, 10=X; 7=VII, 14=XIV.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..503 (complete up to 3999)
• Eric Weisstein's World of Mathematics, Roman Numerals
• Wikipedia, Roman numerals

Crossrefs

Cf. A006968. - Jonathan Vos Post, May 24 2009

Programs

Haskell

a160676 n = a160676_list !! (n-1)
a160676_list = filter (\x -> a006968 x == a006968 (2 * x)) [1..]
-- Reinhard Zumkeller, Apr 14 2013

Maple

for n from 1 to 3999 do if(length(convert(n, roman)) = length(convert(2*n, roman)))then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Mathematica

Select[Range[300],StringLength[RomanNumeral[#]]==StringLength[ RomanNumeral[ 2 #]]&] (* Harvey P. Dale, Apr 29 2022 *)

Formula

{n: A006968(n) = A006968(2n)}. - Jonathan Vos Post, May 24 2009