A356721 Numbers written using exactly two distinct Roman numerals.

4, 6, 7, 8, 9, 11, 12, 13, 15, 19, 21, 22, 23, 25, 29, 31, 32, 33, 35, 39, 40, 51, 52, 53, 55, 60, 70, 80, 90, 101, 102, 103, 105, 110, 120, 130, 150, 190, 201, 202, 203, 205, 210, 220, 230, 250, 290, 301, 302, 303, 305, 310, 320, 330, 350, 390, 400, 501, 502

Offset

1,1

Links

Table of n, a(n) for n=1..59.

Wikipedia, Roman numerals

Example

4, written IV, and 8, written VIII, are terms.
14, written XIV, is not a term.

Mathematica

kmax=502; a={}; For[k=1, k<=kmax, k++, If[Length[DeleteDuplicates[Characters[RomanNumeral[k]]]] == 2, AppendTo[a, k]]]; a (* Stefano Spezia, Aug 26 2022 *)

Prog

(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 roman(n):
    m, c, x, i = n//1000, (n%1000)//100, (n%100)//10, n%10
    return "M"*m + f("CDM", c) + f("XLC", x) + f("IVX", i)
def ok(n): return len(set(roman(n))) == 2
print([k for k in range(503) if ok(k)]) # Michael S. Branicky, Aug 24 2022

Crossrefs

Sequence in context: A043860 A043869 A167524 * A114308 A299411 A079000

Adjacent sequences: A356718 A356719 A356720 * A356722 A356723 A356724

Keyword

nonn,base,fini,easy

Author

Alain Cousquer and Pierre-Hugues Villaume, Aug 24 2022

Status

approved