OFFSET
1,1
COMMENTS
If a number w + x + y + z with w, x, y, z > 0 has w*x = y*z then it is composite.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
John F. Richardson, A Property of Odd Composites, Math Forums, 2012.
EXAMPLE
15=7+8 (partition is x,x+1)
col 1 sum(to products)
1*6=6
2*5=10
3*4=12
col 2 sum(to products)
1*7=7
2*6=12
3*5=15
4*4=16
There is an overlapping product, and the lowest is 12.
This indicates the original N of 15 is composite.
PROG
(PARI) do(n)=my(X=vector(n\4, i, i*(n\2-i)), Y=vector((n+1)\4, i, i*(n\2-i+1)), i=1, j=1); while(X[i]!=Y[j], if(X[i]<Y[j], i++, j++)); X[i]
forstep(n=9, 300, 2, if(!isprime(n), print1(do(n)", "))) \\ Charles R Greathouse IV, Oct 28 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Bill McEachen, Oct 27 2012
STATUS
approved