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.

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

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

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+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

Cf. A006968, A002963, A003587, A036787, A057226.

Cf. A036746, A036786, A036788, A160676, A160677, A199921.

Sequence in context: A259372 A348871 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