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A119281 Number of counting rods to represent n in the ancient Chinese rod numeral system. 1
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; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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.
LINKS
Wikipedia, Chinese numerals
Wikipedia, Counting rods
FORMULA
a(n) = a(-n) = A007953(n) - 4*A102677(n) = A092196(n) + 4*(number of 5s in n).
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A141404 A212176 A070671 * A328943 A173525 A070772
KEYWORD
base,easy,nonn
AUTHOR
Rick L. Shepherd, May 12 2006
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)