A387014 Middle element of the list {1, 2, 3, ..., 2n-1} when elements are sorted lexicographically by their Roman numeral representations.

1, 2, 3, 4, 9, 5, 6, 7, 8, 10, 11, 12, 13, 14, 19, 15, 16, 17, 18, 20, 18, 17, 16, 15, 48, 47, 46, 45, 49, 44, 43, 42, 41, 40, 19, 14, 13, 12, 11, 10, 8, 7, 6, 5, 88, 5, 6, 7, 8, 10, 8, 7, 6, 5, 88, 87, 86, 85, 89, 84, 83, 82, 81, 80, 78, 77, 76, 75, 79, 74, 73, 72, 71, 70

Offset

1,2

Comments

Usual Roman numeral representations are taken as ending at 3999 so that here n <= 2000.

a(21) = 18 is the first repeated element, and 21 is also the least positive integer not in this sequence, which has 1690 distinct terms. More exhaustively, the positive integers not in this sequence are 21 .. 39, 90 .. 100, 200 .. 236, 239 .. 399, 450 .. 484, 489, 900 .. 999, 1005 .. 1008, 1010 .. 1049, 1090 .. 1099, 2001 .. 2099, 2101 .. 2199, 2205 .. 2208, 2210 .. 2249, 2251 .. 2299 and 2400 .. oo (where a .. b means all integers from a to b). - M. F. Hasler, Aug 18 2025

Links

José Hernández, Table of n, a(n) for n = 1..2000

Example

For n = 5, the 2n-1 list elements sorted by Roman numerals are I, II, III, IV, IX, V, VI, VII, VIII and the middle element is IX = 9 = a(5).

Mathematica

Table[SortBy[Range[2*n-1], RomanNumeral][[n]], {n, 100}] (* Misha Lavrov via SeqFan *)

Prog

(Python)
import roman
def A387014(n):
    return roman.fromRoman(sorted(roman.toRoman(k)for k in range(1, 2*n))[n-1]) # M. F. Hasler, Aug 18 2025

Crossrefs

Cf. A036742.

Sequence in context: A124418 A175177 A303951 * A326776 A249746 A112480

Adjacent sequences: A387011 A387012 A387013 * A387015 A387016 A387017

Keyword

base,fini,full,nonn

Author

José Hernández, Aug 13 2025

Status

approved