A119281 Number of counting rods to represent n in the ancient Chinese rod numeral system.

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

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

Table of n, a(n) for n=0..102.

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

Cf. A092196, A007953, A102677.

Sequence in context: A141404 A212176 A070671 * A328943 A173525 A070772

Adjacent sequences: A119278 A119279 A119280 * A119282 A119283 A119284

Keyword

base,easy,nonn

Author

Rick L. Shepherd, May 12 2006

Status

approved