Alain Cousquer - cp's OEIS frontend

User: Alain Cousquer

Alain Cousquer has authored 2 sequences.

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

Alain Cousquer and Pierre-Hugues Villaume, Aug 24 2022

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

Wikipedia, Roman numerals

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 *)

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

A356726 Integers which have in Roman numerals more distinct symbols than any smaller number.

Original entry on oeis.org

1, 4, 14, 44, 144, 444, 1444

Offset: 1

Alain Cousquer, Aug 24 2022

Indices of record highs in A057226.
Smallest number whose Roman notation has exactly n distinct symbols.
The sequence is finite because 1444 is the smallest number using the symbols I,V,X,L,C,D,M.

			For n = 3, a(3) = 14 because 14 = XIV which is the smallest number with 3 symbols in Roman notation.

Cf. A057226, A038378.

kmax=1500; a={}; n=1; For[k=1, k<=kmax, k++, If[Length[DeleteDuplicates[Characters[RomanNumeral[k]]]] == n, AppendTo[a, k]; n++; k=1]]; a (* Stefano Spezia, Aug 26 2022 *)

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User: Alain Cousquer

A356721 Numbers written using exactly two distinct Roman numerals.

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