A003587 Roman numerals with 1 letter, in numerical order; then those with 2 letters, etc.

1, 5, 10, 50, 100, 500, 1000, 2, 4, 6, 9, 11, 15, 20, 40, 51, 55, 60, 90, 101, 105, 110, 150, 200, 400, 501, 505, 510, 550, 600, 900, 1001, 1005, 1010, 1050, 1100, 1500, 2000, 3, 7, 12, 14, 16, 19, 21, 25, 30, 41, 45, 52, 54, 56, 59, 61, 65, 70, 91, 95, 102, 104, 106, 109, 111, 115, 120, 140, 151

Offset: 1

Author

N. J. A. Sloane, J. H. Conway and John Jackson (ab158(AT)freenet.uchsc.edu)

Keywords

• nonn
• base
• fini
• full
• look

Comments

The sequence is finite because 3999 is the largest number that can be written using the symbols I,V,X,L,C,D,M. - J. Lowell, Nov 17 2020

The Romans had symbols for 5000, 10000, 50000, and 100000, but they have no simple equivalents in our current alphabet. See The Book of Numbers, p. 19. The symbol for 100000 is sometimes represented by (((|))). - N. J. A. Sloane, Nov 28 2020

Examples

			Written in Roman numerals, the sequence reads: I, V, X, L, C, D, M, II, IV, VI, IX, XI, XV, XX, XL, LI, LV, LX, XC, CI, CV, CX, CL, CC, CD, DI, DV, DX, DL, DC, CM, MI, MV, MX, MV, MC, MD, MM, III, VII, XII, ... - _M. F. Hasler_, Jan 12 2015
		

References

• J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 19.

Links

• Maxim Skorohodov, Table of n, a(n) for n = 1..3999

Crossrefs

Cf. A003588, A036746, A061493, A006968.

Programs

Mathematica

A003587full = SortBy[Range[3999], StringLength[RomanNumeral[#]] &];
A003587full[[;;100]] (* Paolo Xausa, Mar 19 2024 *)

PARI

for(d=1,4,for(n=d,d*1000,A006968(n)==d && print1(n","))) \\ M. F. Hasler, Jan 12 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 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 afull():
    return sorted(list(range(1, 4000)), key=lambda x: (len(roman(x)), x))
print(afull()) # Michael S. Branicky, Dec 04 2022

Extensions

More terms from M. F. Hasler, Jan 12 2015