1a. Re: Composite integer function

Posted by: "Yann Guidon"

whygee@... yasep16

Date: Wed Nov 18, 2009 9:02 am ((PST))

Hello Kermit,

it seems that my emails can't reach you

due to some unexplainable blacklist on some router near you.

So I answer on the list :

can you please elaborate ?

Hello Yann.

..........s=1... s=2 ... s=3 ... s=4 .. s=5 . s=6

m=1 015 021 027 033 039 045

m=2 035 045 055 065 075 085

m=3 063 077 091 105 119 133

m=4 099 117 135 153 171 189

m=5 143 165 187 209 231 253

m=6 195 221 247 273 299 325

The table extends to arbitrarily large values.

Table entry at row m and column s is (2 * m + 1) * (2 * m + 1 + 2 * s)

For example, 153 at row 4 and column 4 is (2 * 4 + 1) * (2 * 4 + 1 + 2 *

4) = 9 * 17

Adjacent table entries have an additive relationship to each other.

For example 117 in row 4, column 2,

and 165 in row 5, column 2,

are related as follows.

165 = 117 + 48 = 117 + 8 * 4 + 4 * 2 + 8

Table entry in row (m+1) and column s

= table entry in row (m) and column s,

plus 8 times row number m,

plus 4 times column number s,

plus 8.

There is a similar addition rule to calculate entries in the next column

over.

The extended table lists all the non-square odd composite positive integers,

and has both additive and multiplicative rules for determining

table entries.

It is not trivial to find the location of a large number in the table.

The easiest way to find a large integer in the table is to factor the

integer.

However, if some other algorithm for locating a given number in the

table is developed, that algorithm would also be a factoring algorithm.

Kermit.