

A061493


Roman numerals written using 1 for I, 2 for V, 3 for X, 4 for L, 5 for C, 6 for D, 7 for M.


19



1, 11, 111, 12, 2, 21, 211, 2111, 13, 3, 31, 311, 3111, 312, 32, 321, 3211, 32111, 313, 33, 331, 3311, 33111, 3312, 332, 3321, 33211, 332111, 3313, 333, 3331, 33311, 333111, 33312, 3332, 33321, 333211, 3332111, 33313, 34, 341, 3411, 34111, 3412
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OFFSET

1,2


COMMENTS

From Daniel Forgues, Jan 16 2015: (Start)
The Romans did not have 0 as a number, which is why there was no year zero (1 B.C. is followed by 1 A.D.).
The initial "N" (nulla, meaning "nothing") was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725. (End)
3999 (MMMCMXCIX) is the largest decimal number that has a welldefined Roman numeral representation. Therefore the sequence deliberately stops there to avoid the ambiguous representations of larger numbers.  Jamie Robert Creasey, May 01 2021


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..3999
Gerard Schildberger, The first 3999 numbers in Roman numerals
Eric Weisstein's World of Mathematics, Roman Numerals
Wikipedia, Roman numerals
Wikipedia, 0 (number) in classical antiquity


FORMULA

a(n)=i <=> A003587(i)=n, for i in {1,...,7}, i.e., A061493 is a left inverse of A003587 on {1,...,7}.  M. F. Hasler, Jan 12 2015


EXAMPLE

a(14) = 312 because 14 = XIV in Roman, and I,V,X are coded as 1,2,3 respectively.
a(66)= 4321, LXVI is 50+10+5+1= 66, a(44)=3412, XLIV is 10+501+5= 44


MATHEMATICA

Array[FromDigits[Characters@ RomanNumeral[#] /. {"I" > 1, "V" > 2, "X" > 3, "L" > 4, "C" > 5, "D" > 6, "M" > 7}] &, 44] (* Michael De Vlieger, May 01 2021 *)


PROG

(Haskell)
a061493 n = read $ r 1 [] n :: Integer where
r _ roms 0 = roms
r p roms z = case p of
1 > r 2 (d '1' '2' '3' m) z'
2 > r 3 (d '3' '4' '5' m ++ roms) z'
3 > r 4 (d '5' '6' '7' m ++ roms) z'
4 > replicate z '7' ++ roms
where (z', m) = divMod z 10
d i j k c =
[[], [i], [i, i], [i, i, i], [i, j], [j], [j, i], [j, i, i], [j, i, i, i], [i, k]] !! c
 Reinhard Zumkeller, Apr 14 2013
(PARI) {A061493(n, s="", c=[1000, 7, 900, 57, 500, 6, 400, 56, 100, 5, 90, 35, 50, 4, 40, 34, 10, 3, 9, 13, 5, 2, 4, 12, 1, 1])= forstep(i=1, #c, 2, while(n>=c[i], n=c[i]; s=Str(s, c[i+1]))); eval(s)} \\ M. F. Hasler, Jan 11 2015


CROSSREFS

Cf. A006968, A002963, A003587, A036787, A057226.
Cf. A036746, A036786, A036788, A160676, A160677, A199921.
Sequence in context: A055016 A259372 A004287 * A093788 A327992 A204847
Adjacent sequences: A061490 A061491 A061492 * A061494 A061495 A061496


KEYWORD

easy,nonn,base


AUTHOR

Frank Ellermann, Jun 12 2001


EXTENSIONS

0 removed again by Georg Fischer, Jan 20 2019


STATUS

approved



