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Search: id:A118121
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| A118121 |
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Roman numeral complexity of n. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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EXAMPLE
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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].
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CROSSREFS
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Cf. A005245, A006968, A092196.
Sequence in context: A084199 A030314 A098236 this_sequence A006968 A058207 A105969
Adjacent sequences: A118118 A118119 A118120 this_sequence A118122 A118123 A118124
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 12 2006
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