|
|
A328971
|
|
Numerator of the fraction (hypotenuse - difference of legs) / (sum of legs - hypotenuse) of the n-th primitive Pythagorean triangle.
|
|
2
|
|
|
2, 3, 5, 4, 7, 7, 5, 9, 6, 7, 9, 11, 11, 7, 8, 9, 11, 13, 8, 13, 15, 13, 9, 10, 11, 12, 15, 10, 17, 11, 12, 15, 13, 17, 19, 11, 17, 13, 19, 17, 19, 12, 13, 14, 21, 15, 19, 16, 21, 13, 14, 23, 19, 16, 23, 17, 21, 14, 25, 23, 16, 17, 25, 21, 23, 15, 19, 16, 17, 18, 23, 27, 25, 19, 20, 16, 17, 23, 18
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
a(n) / A328972(n) should contain all reduced fractions between 1 and sqrt(2) + 1 without duplicates.
a(n) is built from the difference between the length of the hypotenuse (A020882) and the difference between the two legs (A120682) of the n-th primitive Pythagorean triangle.
A328972(n) (denominators) is built from the difference between the sum of the length of the legs (A120681) and the hypotenuse of the n-th primitive Pythagorean triangle.
Then both numbers are divided by their GCD to get the reduced fraction.
All primitive Pythagorean triangles are sorted first on hypotenuse, then on long leg.
|
|
LINKS
|
|
|
EXAMPLE
|
For n=2 we need the 2nd primitive Pythagorean triangle:
5,12,13
^ ^ We calculate the difference between the two small numbers: 12-5=7.
^ And to get our numerator we subtract 7 from the hypotenuse length: 13-7=6.
^ ^ Then we calculate the sum of the two small numbers: 5+12=17.
^ We subtract 13 from this sum to get the denominator: 17-13=4.
This gives us the fraction 6/4, and in reduced form 3/2.
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|