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Search: id:A119281
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| A119281 |
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Number of counting rods to represent n in the ancient Chinese rod numeral system. |
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+0
1
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| 0, 1, 2, 3, 4, 5, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 7, 8, 9, 10, 1, 2, 3
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contrast with A092196, the number of letters to represent n in ancient Roman numerals. Negative numbers were represented by the same number of rods but usually of a different color (usually black rods with red rods for positive numbers). It's unclear to me whether 0 itself was ever formally considered represented by the absence of all counting rods, but it does seem reasonable that a(0)=0 from the example below.
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LINKS
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Wikipedia, Chinese numerals
Wikipedia, Counting rods
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FORMULA
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a(n) = a(-n) = A007953(n) - 4*A102677(n) = A092196(n) + 4*(number of 5s in n).
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EXAMPLE
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a(105) = 6 because 105 was represented on a counting board by placing one counting rod in the compartment for hundreds, no rods where those representing tens were normally placed and five rods in the units compartment.
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PROGRAM
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(PARI) a(n)= tmp=abs(n); r=0; l=length(Str(tmp)); for(k=1, l, d=tmp-(tmp\10)*10; tmp=tmp\10; if(d<6, r=r+d, r=r+d-4)); r
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CROSSREFS
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Cf. A092196, A007953, A102677.
Sequence in context: A165072 A141404 A070671 this_sequence A070772 A094937 A161768
Adjacent sequences: A119278 A119279 A119280 this_sequence A119282 A119283 A119284
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KEYWORD
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base,easy,nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 12 2006
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