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Search: id:A123060
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| A123060 |
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Least positive integer k such than n has the same number of characters in base k and in Roman numeral representation, or 0 if no such k exists. |
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+0
1
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| 1, 1, 1, 4, 6, 6, 2, 2, 9, 11, 11, 3, 2, 3, 15, 4, 0, 2, 3, 20, 3, 0, 2, 0, 5, 0, 2, 0, 0, 4, 3, 0, 2, 0, 3, 0, 2, 0, 0, 40, 4, 3, 0, 3, 4, 3, 0, 2, 3, 51, 51
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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Gerard Schildberger, The first 3999 numbers in Roman numerals.
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FORMULA
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a(n) = min{k: StringLength(n base k) = StringLength(Roman(n))}, or 0 if no such k exists. a(n) = min{k: A006968(n) = 1 + floor(log_b(n))}, or 0 if no such k exists.
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EXAMPLE
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a(1) = 1 since Roman(1) = I and 1(base 1) have the same (1) number of characters.
a(4) = 4 since Roman(4) = IV and 10(base 4) have the same (2) number of characters.
a(8) = 2 since Roman(8) = VIII and 1000(base 2) have the same (4) number of characters.
a(10) = 11 since Roman(10) = X and X(base 11) have the same (1) number of characters.
a(11) = 11 since Roman(11) = XI and 10(base 11) have the same (2) number of characters.
a(12) = 3 since Roman(12) = XII and 110(base 3) have the same (3) number of characters.
a(17) = 0 because Roman(17) = XVII has 4 characters, while 17 = 10001(base 2) has 5 characters and 17 = 122(base 3) has 3 characters.
a(30) = 4 because Roman(30) = XXX has 3 characters, as do 110(base 5) and 132(base 4), but Min{4,5} = 4.
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CROSSREFS
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Cf. A006968.
Sequence in context: A009456 A009465 A119858 this_sequence A130753 A021686 A019923
Adjacent sequences: A123057 A123058 A123059 this_sequence A123061 A123062 A123063
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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), Sep 26 2006
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