This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118121 #10 Sep 13 2024 00:39:38
%S A118121 1,2,3,2,1,2,3,4,2,1,2,3,4,3,2,3,4,4,3,2,3,4,5,4,3,4,5,5,4,3,4,5,5,5,
%T A118121 4,4,5,5,5,2,3,4,5,4,3,4,5,6,4,1,2,3,4,3,2,3,4,5,3,2,3,4,5,4,3,4,5,6,
%U A118121 4,3,4,5,6,5,4,5,5,6,5,4,4,5,6,5,5,6,6,6,6,2,3,4,5,4,3,4,5,6,4,1,2,3
%N A118121 Roman numeral complexity of n.
%C A118121 The least number of letters {I, V, X, L, C, D, M} needed to represent n by an expression with conventional Roman numerals, addition, multiplication and parentheses. a(n) <= A006968(n) and a(n) <= A005245(n). Conventional Roman numerals are very efficient at reducing complexity from number of letters in "old style" Roman numerals (A092196) and more primitive representations. In all but two examples shown (38, 88) the use of {+,*} reduces the representation by a single symbol (counting + and *); in these two it saves 2 symbols. In an alternate history, complexity theory and minimum description length could have been invented by Gregorius Catin.
%H A118121 <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a>
%e A118121 a(n) < A006968(n) for these examples. Here "<" means less in letter count:
%e A118121 a(18) = 4 [IX + IX < XVIII]; a(28) = 5 [XIV * II < XXVIII]; a(33) = 5 [XI * III < XXXIII]; a(36) = 4 [VI * VI < XXXVI]; a(37) = 5 [VI * VI + I < XXXVII]; a(38) = 5 [XIX * II < XXXVIII]; a(77) = 5 [XI * VII < LXXVII]; a(78) = 6 [XIII * VI < LXXVIII]; a(81) = 4 [IX * IX < LXXXI]; a(82) = 5 [XLI * II < LXXXII]; a(83) = 6 [XLI * II + I < LXXXIII]; a(84) = 5 [XX * IV < LXXXIV]; a(87) = 6 [IX * IX + VI < LXXXVII]; a(88) = 6 [XI * VIII < LXXXVIII].
%Y A118121 Cf. A005245, A006968, A092196.
%K A118121 base,easy,nonn
%O A118121 1,2
%A A118121 _Jonathan Vos Post_, May 12 2006