|
%I #3 Mar 30 2012 17:36:44
%S 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,
%T 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,
%U 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
%N Number of counting rods to represent n in the ancient Chinese rod numeral system.
%C 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 Wikipedia, <a href="http://www.wikipedia.org/wiki/Chinese_numerals">Chinese numerals</a>
%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Rod_numerals">Counting rods</a>
%F a(n) = a(-n) = A007953(n) - 4*A102677(n) = A092196(n) + 4*(number of 5s in n).
%e 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 (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 Cf. A092196, A007953, A102677.
%K base,easy,nonn
%O 0,3
%A _Rick L. Shepherd_, May 12 2006
|
