A097753 Table read by antidiagonals of least integer "mod 4 prime signatures" k ordered by number of Pythagorean triples with hypotenuse = k.

1, 2, 5, 3, 10, 25, 4, 15, 50, 125, 6, 20, 75, 250, 65, 8, 30, 100, 375, 130, 3125, 9, 40, 150, 500, 195, 6250, 15625, 12, 45, 200, 750, 260, 9375, 31250, 325, 16, 60, 225, 1000, 390, 12500, 46875, 650, 390625, 18, 80, 300, 1125, 520, 18750, 62500, 975

Offset

1,2

Comments

See A097751 for definition of "mod 4 prime signature".

Row 0 of table represents "mod 4 prime signature" values k such that no PTs have hypotenuse=k.

Row n of table, n>0, represents "mod 4 prime signature" values k such that n PTs have hypotenuse=k.

Links

Table of n, a(n) for n=1..53.

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Example

Table begins:
0: 1,2,3,4,6,8,9,12,16,18,21,...
1: 5,10,15,20,30,40,45,60,80,90,105,...
2: 25,50,75,100,150,200,225,300,400,450,525,...
3: 125,250,375,500,750,1000,1125,1500,2000,2250,2625,...
4: 65,130,195,260,390,520,585,625,780,1040,1170,...
5: 3125,6250,9375,12500,18750,25000,28125,37500,...
6: 15625,31250,46875,62500,93750,125000,140625,...
7: 325,650,975,1300,1950,2600,2925,3900,5200,...
8: 390625,781250,1171875,1562500,2343750,...
9: 1953125,3906250,5859375,7812500,11718750,...
10: 1625,3250,4875,6500,9750,13000,14625,19500,...

Crossrefs

Cf. A097751, A097752, A097754, A097755, A097756.

Sequence in context: A297442 A277709 A138765 * A120860 A259971 A091809

Adjacent sequences: A097750 A097751 A097752 * A097754 A097755 A097756

Keyword

nonn,tabl

Author

Ray Chandler, Aug 26 2004

Extensions

Correct offset. Ray Chandler, Jan 15 2013

Status

approved