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%I #25 Mar 03 2024 17:18:07
%S 1,2,3,4,5,6,9,10,11,19,20,30,40,50,60,90,100,110,190,200,300,400,500,
%T 600,900,1000,1100,1900,2000,3000
%N Numbers whose Roman numeral representation, reversed, is a Roman numeral.
%C A subset of this is A078715, palindromic Roman numerals. These are not "old style" Roman numerals (where 4 = IIII).
%C The sequence contains only values less than 4000, see A078715 for a discussion of the Roman 4M-problem.
%H Stephanus Gibbs, <a href="http://www.softhawkway.com/rcalc.htm">Roman Numeral and Date Conversion</a>
%H Gerard Schildberger, <a href="/A006968/a006968.txt">The first 3999 numbers in Roman numerals</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RomanNumerals.html">Roman Numerals</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Roman_numerals">Roman numerals</a>
%e a(1) = 1 because Roman(1) = I and Reversal(I) = I, which is Roman.
%e a(4) = 4 because Roman(4) = IV and Reversal(IV) = VI, which is Roman.
%e a(10) = 19 because Roman(19) = XIX which is a palindromic Roman numeral.
%e a(27) = 900 because Roman(900) = CM and Reversal(CM) = MC, which is Roman.
%e 40 == XL -> LX == 60, therefore 40 and 60 are terms.
%e 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 Select[Range[3000], RomanNumeral[FromRomanNumeral[#]] == # & [StringReverse[RomanNumeral[#]]] &] (* _Paolo Xausa_, Mar 03 2024 *)
%o (Haskell)
%o a093703 n = a093703_list !! (n-1)
%o a093703_list = filter
%o ((`elem` map a061493 [1..3999]) . a004086 . a061493) [1..]
%o -- _Reinhard Zumkeller_, Apr 14 2013
%Y Cf. A078715 (palindromic Roman numerals), A061493.
%K nonn,base,fini,full
%O 1,2
%A _Reinhard Zumkeller_, May 17 2004
%E Added sections of text from the erroneous A123054. - _N. J. A. Sloane_, Apr 15 2013
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