A003587 - OEIS

%I #37 Mar 19 2024 11:47:49

%S 1,5,10,50,100,500,1000,2,4,6,9,11,15,20,40,51,55,60,90,101,105,110,

%T 150,200,400,501,505,510,550,600,900,1001,1005,1010,1050,1100,1500,

%U 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

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

%C 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

%C 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

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

%H Maxim Skorohodov, <a href="/A003587/b003587.txt">Table of n, a(n) for n = 1..3999</a>

%e 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

%t A003587full = SortBy[Range[3999], StringLength[RomanNumeral[#]] &];

%t A003587full[[;;100]] (* _Paolo Xausa_, Mar 19 2024 *)

%o (PARI) for(d=1,4,for(n=d,d*1000,A006968(n)==d && print1(n","))) \\ _M. F. Hasler_, Jan 12 2015

%o (Python)

%o def f(s, k):

%o     return s[:2] if k==4 else (s[1]*(k>=5)+s[0]*(k%5) if k<9 else s[0]+s[2])

%o def roman(n):

%o     m, c, x, i = n//1000, (n%1000)//100, (n%100)//10, n%10

%o     return "M"*m + f("CDM", c) + f("XLC", x) + f("IVX", i)

%o def afull():

%o     return sorted(list(range(1, 4000)), key=lambda x: (len(roman(x)), x))

%o print(afull()) # _Michael S. Branicky_, Dec 04 2022

%Y Cf. A003588, A036746, A061493, A006968.

%K nonn,base,fini,full,look

%O 1,2

%A _N. J. A. Sloane_, _J. H. Conway_ and John Jackson (ab158(AT)freenet.uchsc.edu)

%E More terms from _M. F. Hasler_, Jan 12 2015