A093703 Numbers whose Roman numeral representation, reversed, is a Roman numeral.

1, 2, 3, 4, 5, 6, 9, 10, 11, 19, 20, 30, 40, 50, 60, 90, 100, 110, 190, 200, 300, 400, 500, 600, 900, 1000, 1100, 1900, 2000, 3000

Offset: 1

Author

Reinhard Zumkeller, May 17 2004

Keywords

• nonn
• base
• fini
• full

Comments

A subset of this is A078715, palindromic Roman numerals. These are not "old style" Roman numerals (where 4 = IIII).

The sequence contains only values less than 4000, see A078715 for a discussion of the Roman 4M-problem.

Examples

			a(1) = 1 because Roman(1) = I and Reversal(I) = I, which is Roman.
a(4) = 4 because Roman(4) = IV and Reversal(IV) = VI, which is Roman.
a(10) = 19 because Roman(19) = XIX which is a palindromic Roman numeral.
a(27) = 900 because Roman(900) = CM and Reversal(CM) = MC, which is Roman.
40 == XL -> LX == 60, therefore 40 and 60 are terms.
1999 is not in the sequence because "MIM" is not a well-formed Roman numeral for 1999, although it looks like one; see Schildberger.
		

Links

• Stephanus Gibbs, Roman Numeral and Date Conversion
• Gerard Schildberger, The first 3999 numbers in Roman numerals
• Eric Weisstein's World of Mathematics, Roman Numerals
• Wikipedia, Roman numerals

Crossrefs

Cf. A078715 (palindromic Roman numerals), A061493.

Programs

Haskell

a093703 n = a093703_list !! (n-1)
a093703_list = filter
   ((`elem` map a061493 [1..3999]) . a004086 . a061493) [1..]
-- Reinhard Zumkeller, Apr 14 2013

Mathematica

Select[Range[3000], RomanNumeral[FromRomanNumeral[#]] == # & [StringReverse[RomanNumeral[#]]] &] (* Paolo Xausa, Mar 03 2024 *)

Extensions

Added sections of text from the erroneous A123054. - N. J. A. Sloane, Apr 15 2013