OFFSET
1,1
COMMENTS
If an odd number is of the form a^2 + b^2, then a and b must be one of the following forms.
a=4n+1, b=4m so that a^2+b^2 = 16(m^2+n^2) + 8n + 1 of form 4k1+1
a=4n+3, b=4m a^2+b^2 = 16(m^2+n^2) + 24n + 1 of form 4k2+1
a=4n+1, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(n+2m ) + 5 of form 4k3+1
a=4n+3, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(3n+2m) + 13 of form 4k4+1
The sequences built using these 4 forms produce all prime numbers of the form 4k+1.This particular sequence is a=4n+1, b=4m.
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Oct 11 2003
STATUS
approved