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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 (list; graph; refs; listen; history; text; internal format)
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 well-defined Roman numeral representation. Therefore the sequence deliberately stops there to avoid the ambiguous representations of larger numbers. - Jamie Robert Creasey, May 01 2021
LINKS
Eric Weisstein's World of Mathematics, Roman Numerals
Wikipedia, Roman numerals
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+50-1+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
(Python)
def f(s, k):
return s[:2] if k==4 else (s[1]*(k>=5)+s[0]*(k%5) if k<9 else s[0]+s[2])
def a(n):
m, c, x, i = n//1000, (n%1000)//100, (n%100)//10, n%10
return int("7"*m + f("567", c) + f("345", x) + f("123", i))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Aug 24 2022
CROSSREFS
Sequence in context: A259372 A348871 A004287 * A093788 A327992 A204847
KEYWORD
easy,nonn,base
AUTHOR
Frank Ellermann, Jun 12 2001
EXTENSIONS
0 removed again by Georg Fischer, Jan 20 2019
STATUS
approved

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Last modified June 24 19:28 EDT 2024. Contains 373690 sequences. (Running on oeis4.)