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Search: id:A123054
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| A123054 |
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Numbers whose Roman numeral representation, reversed, is a Roman numeral. |
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+0
3
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| 1, 2, 3, 4, 5, 6, 9, 10, 11, 19, 20, 30, 40, 49, 50, 51, 60, 90, 100, 110, 190, 200, 300, 400, 500, 600, 900, 1000, 1100, 1900, 2000, 3000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A subset of this is A078715 Palindromic Roman numerals. Not "Old style" Roman numerals (where 4 = IIII).
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LINKS
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Gerard Schildberger, The first 3999 numbers in Roman numerals.
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FORMULA
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{n such that Reversal(Roman(n)) = m and Roman^-1(Reversal(m)) = j for some integer j}. {n such that Roman^-1(Reversal(Roman(n))) is an element of {Roman(k)}}.
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EXAMPLE
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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.
1999 is not in the sequence because "MIM" is not a well-formed Roman numeral for 1999, although it looks like one; see Schildberger.
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CROSSREFS
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Cf. A078715.
Sequence in context: A119356 A137582 A116965 this_sequence A093703 A117073 A063952
Adjacent sequences: A123051 A123052 A123053 this_sequence A123055 A123056 A123057
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KEYWORD
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base,easy,fini,full,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 26 2006
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