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 A118121 Roman numeral complexity of n. 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE a(n) < A006968(n) for these examples. Here "<" means less in letter count: 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]. CROSSREFS Cf. A005245, A006968, A092196. Sequence in context: A269624 A098236 A152978 * A006968 A058207 A105969 Adjacent sequences:  A118118 A118119 A118120 * A118122 A118123 A118124 KEYWORD base,easy,nonn AUTHOR Jonathan Vos Post, May 12 2006 STATUS approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)