Search: id:A119281
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%I A119281
%S A119281 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,
%T A119281 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,
%U A119281 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
%N A119281 Number of counting rods to represent n in the ancient Chinese rod numeral 
               system.
%C A119281 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.
%H A119281 Wikipedia, <a href="http://www.wikipedia.org/wiki/Chinese_numerals">Chinese 
               numerals</a>
%H A119281 Wikipedia, <a href="http://www.wikipedia.org/wiki/Rod_numerals">Counting 
               rods</a>
%F A119281 a(n) = a(-n) = A007953(n) - 4*A102677(n) = A092196(n) + 4*(number of 
               5s in n).
%e A119281 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.
%o A119281 (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
%Y A119281 Cf. A092196, A007953, A102677.
%Y A119281 Sequence in context: A165072 A141404 A070671 this_sequence A070772 A094937 
               A161768
%Y A119281 Adjacent sequences: A119278 A119279 A119280 this_sequence A119282 A119283 
               A119284
%K A119281 base,easy,nonn
%O A119281 0,3
%A A119281 Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 12 2006

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