A097754 Table read by antidiagonals of least integer "mod 4 prime signatures" k ordered by number of primitive Pythagorean triples with hypotenuse = k.

1, 2, 5, 3, 25, 65, 4, 125, 325, 1105, 6, 625, 1625, 5525, 32045, 8, 3125, 4225, 27625, 160225, 1185665, 9, 15625, 8125, 71825, 801125, 5928325, 48612265, 10, 78125, 21125, 138125, 2082925, 29641625, 243061325, 2576450045, 12, 390625, 40625

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 PPTs have hypotenuse=k.

Row n of table, n>0, represents "mod 4 prime signature" values k such that 2^(n-1) PPTs have hypotenuse=k.

Links

Table of n, a(n) for n=1..39.

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Example

Table begins:
0: 1,2,3,4,6,8,9,10,12,15,16,18,20,21,24,27,30,...
1: 5,25,125,625,3125,15625,78125,390625,1953125,...
2: 65,325,1625,4225,8125,21125,40625,105625,203125,...
4: 1105,5525,27625,71825,138125,359125,690625,1221025,...
8: 32045,160225,801125,2082925,4005625,10414625,20028125,...
16: 1185665,5928325,29641625,77068225,148208125,385341125,...
32: 48612265,243061325,1215306625,3159797225,6076533125,...
64: 2576450045,12882250225,64411251125,167469252925,...
128: 157163452745,785817263725,3929086318625,10215624428425,...
256: 11472932050385,57364660251925,286823301259625,...

Crossrefs

Cf. A097751, A097752, A097753, A097755, A097756.

Row 1 is A000351 except for starting point.

Sequence in context: A309080 A058357 A176613 * A122992 A051497 A246556

Adjacent sequences: A097751 A097752 A097753 * A097755 A097756 A097757

Keyword

nonn,tabl

Author

Ray Chandler, Aug 26 2004

Extensions

Correct offset. Ray Chandler, Jan 15 2013

Status

approved