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

1,1

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A169586 A023229 A176983 * A169690 A144300 A258430

Adjacent sequences: A160673 A160674 A160675 * A160677 A160678 A160679

Keyword

nonn,easy,base

Author

Claudio Meller, May 23 2009

Status

approved