OFFSET
1,2
COMMENTS
Eta numbers are the odd complement of A020882.
Properties: A PPT hypotenuse has form (4k+1), but the converse is not true. Thus Eta numbers fall into two classes: #1 Odd integers which do not have form (4k+1), #2 Odd integers of form (4k+1) which are not members of A020882.
Eta numbers >1 can be the leg of PPT[a,b,c] but not a hypotenuse, while members of A020882 can be both. By Fermat's theorem, class #2 eta numbers are not prime.
LINKS
H. Lee Price and Frank R. Bernhart, Pythagorean Triples and a New Pythagorean Theorem, arXiv:math.HO/0701554, (2007).
Frank Bernhart and H. Lee Price, Heron's Formula, Descartes Circles and Pythagorean Triangles, arXiv:math.MG/0701624, (2007).
FORMULA
Class #1 a(n) = E because E is nonnegative, odd and not equal to (4k+1). Class #2 a(n) = E because E=(4k+1) (not class #1) but is not a member of A020882.
EXAMPLE
Class #1 a(6) = E because E is nonnegative, odd and not equal to (4k+1).
Class #2 a(4) = E because E is nonnegative, odd and E=(4k+1) but is not a member of A020882.
CROSSREFS
KEYWORD
nonn
AUTHOR
H. Lee Price, Jan 29 2007, corrected Feb 03 2007
STATUS
approved