Listing the entire sequence would consume 83MB worth of characters.

The sequence begins as follows (1-100)

1-10: i, ii, iii, iv, v, vi, vii, viii, ix, x

11-20: xi, xii, xiii, xiv, xv, xvi, xvii, xviii, xix, xx

21-30: xxi, xxii, xxiii, xxiv, xxv, xxvi, xxvii, xxviii, xxix, xxx

31-40: xxxi, xxxii, xxxiii, xxxiv, xxxv, xxxvi, xxxvii, xxxviii, xxxix, xl

41-50: xli, xlii, xliii, xliv, xlv, xlvi, xlvii, xlviii, xlix, l

51-60: li, lii, liii, liv, lv, lvi, lvii, lviii, lix, lx

61-70: lxi, lxii, lxiii, lxiv, lxv, lxvi, lxvii, lxviii, lxix, lxx

71-80: lxxi, lxxii, lxxiii, lxxiv, lxxv, lxxvi, lxxvii, lxxviii, lxxix, lxxx

81-90: lxxxi, lxxxii, lxxxiii, lxxxiv, lxxxv, lxxxvi, lxxxvii, lxxxviii, lxxxix, xc

91-100: xci, xcii, xciii, xciv, xcv, xcvi, xcvii, xcviii, xcix, c

The sequence then repeats, with an additional c prefixed for each hundred, until we reach 400 which replaces the ccc prefix with a cd prefix. We then continue to 500 which reduces the prefix to just d, then dc for 600, dcc for 700, dccc for 800, mc for 900 and m for 1,000. The sequence starts again with an m prefix until we reach 2000, which is mm, then mmm for 3,000. The sequence ends at 3,999 because the accepted convention is to never repeat a symbol more than 3 times in succession.

To give you an idea of the format, the final 100 numbers are:

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