cp's OEIS Frontend

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

%I A093703 #26 Feb 16 2025 08:32:53
%S A093703 1,2,3,4,5,6,9,10,11,19,20,30,40,50,60,90,100,110,190,200,300,400,500,
%T A093703 600,900,1000,1100,1900,2000,3000
%N A093703 Numbers whose Roman numeral representation, reversed, is a Roman numeral.
%C A093703 A subset of this is A078715, palindromic Roman numerals. These are not "old style" Roman numerals (where 4 = IIII).
%C A093703 The sequence contains only values less than 4000, see A078715 for a discussion of the Roman 4M-problem.
%H A093703 Stephanus Gibbs, <a href="http://www.softhawkway.com/rcalc.htm">Roman Numeral and Date Conversion</a>
%H A093703 Gerard Schildberger, <a href="/A006968/a006968.txt">The first 3999 numbers in Roman numerals</a>
%H A093703 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RomanNumerals.html">Roman Numerals</a>
%H A093703 Wikipedia, <a href="http://en.wikipedia.org/wiki/Roman_numerals">Roman numerals</a>
%e A093703 a(1) = 1 because Roman(1) = I and Reversal(I) = I, which is Roman.
%e A093703 a(4) = 4 because Roman(4) = IV and Reversal(IV) = VI, which is Roman.
%e A093703 a(10) = 19 because Roman(19) = XIX which is a palindromic Roman numeral.
%e A093703 a(27) = 900 because Roman(900) = CM and Reversal(CM) = MC, which is Roman.
%e A093703 40 == XL -> LX == 60, therefore 40 and 60 are terms.
%e A093703 1999 is not in the sequence because "MIM" is not a well-formed Roman numeral for 1999, although it looks like one; see Schildberger.
%t A093703 Select[Range[3000], RomanNumeral[FromRomanNumeral[#]] == # & [StringReverse[RomanNumeral[#]]] &] (* _Paolo Xausa_, Mar 03 2024 *)
%o A093703 (Haskell)
%o A093703 a093703 n = a093703_list !! (n-1)
%o A093703 a093703_list = filter
%o A093703    ((`elem` map a061493 [1..3999]) . a004086 . a061493) [1..]
%o A093703 -- _Reinhard Zumkeller_, Apr 14 2013
%Y A093703 Cf. A078715 (palindromic Roman numerals), A061493.
%K A093703 nonn,base,fini,full
%O A093703 1,2
%A A093703 _Reinhard Zumkeller_, May 17 2004
%E A093703 Added sections of text from the erroneous A123054. - _N. J. A. Sloane_, Apr 15 2013