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

1,2

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A003588, A036746, A061493, A006968.

Sequence in context: A271275 A270100 A271287 * A268100 A205884 A032088

Adjacent sequences: A003584 A003585 A003586 * A003588 A003589 A003590

Keyword

nonn,base,fini,full,look

Author

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

Extensions

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

Status

approved