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A093703 Numbers whose Roman numeral representation, reversed, is a Roman numeral. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..30.

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

EXAMPLE

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.

PROG

(Haskell)

a093703 n = a093703_list !! (n-1)

a093703_list = filter

   ((`elem` map a061493 [1..3999]) . a004086 . a061493) [1..]

-- Reinhard Zumkeller, Apr 14 2013

CROSSREFS

Cf. A078715 (palindromic Roman numerals), A061493.

Sequence in context: A116965 A306975 A123054 * A117073 A063952 A277025

Adjacent sequences:  A093700 A093701 A093702 * A093704 A093705 A093706

KEYWORD

nonn,base,fini,full

AUTHOR

Reinhard Zumkeller, May 17 2004

EXTENSIONS

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

STATUS

approved

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Last modified June 20 14:54 EDT 2021. Contains 345165 sequences. (Running on oeis4.)