For each fixed value of i, we call the expression contained within the summation sign in equation (1) a Z/i layer. Normally, to compute 100 correct terms in Comp(z), the upperbound of i should be set to 100. However, from knowledge of periodicities of summated sequences, we know that evem of half the Z/i layers are used, i.e. i=2..50, the composite number sequence will still be correct up to the full range albeit that the numerator coefficients in the upperhalf of the sequence will be smaller. Since we are only interested in the composites themselves, the errors in these coefficients are not that important. Hence by the definition of throwing power, Comp(z) has a throwing power of 100/50 = 2.

The formula for Oddcomp(z) has already been previously developed [5]. In this paper, the throwing power of Oddcomp(z) is investigated. It is known that if Oddcomp(z) is fully expanded starting from i = 1, it will predict deterministically the odd composite sequence but this demands considerable computing resources. Since most of the time such a sequence would be normalised using Normc( ), we could have ignored the accuracy of the numerator coefficients or duplicity factors. Oddcomp1(z) is expanded using the range of i = 1..10000 for computations which will ensure that all odd composite terms in the sequence are correct. This will be used to benchmark an Oddcomp2(z) sequence which is similarly expanded using i = 1..40. The expansions are term by term compared in order to discover at what point will the first miss occur in the Oddcomp(z0 sequence.


2. The Test Procedures

Step(1): We expand Oddcomp(z) by Maple V R 3 to 10000 terms using equation (2).

Oddcomp1(z):=sort(series(sum(1/(z^(2*i+1)*(z^(2*(2*i+1))-1)),i=1..10000), z=infinity,10000)); ..........................................................................(2).

The expansions are only partially recorded for page economy. Note that the integer 6889 written in bold font is the first oddcomposite integer missing in Oddcomp2(z) of equations (4) and (5).