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A097754 Table read by antidiagonals of least integer "mod 4 prime signatures" k ordered by number of primitive Pythagorean triples with hypotenuse = k. 6

%I

%S 1,2,5,3,25,65,4,125,325,1105,6,625,1625,5525,32045,8,3125,4225,27625,

%T 160225,1185665,9,15625,8125,71825,801125,5928325,48612265,10,78125,

%U 21125,138125,2082925,29641625,243061325,2576450045,12,390625,40625

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

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

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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>

%e Table begins:

%e 0: 1,2,3,4,6,8,9,10,12,15,16,18,20,21,24,27,30,...

%e 1: 5,25,125,625,3125,15625,78125,390625,1953125,...

%e 2: 65,325,1625,4225,8125,21125,40625,105625,203125,...

%e 4: 1105,5525,27625,71825,138125,359125,690625,1221025,...

%e 8: 32045,160225,801125,2082925,4005625,10414625,20028125,...

%e 16: 1185665,5928325,29641625,77068225,148208125,385341125,...

%e 32: 48612265,243061325,1215306625,3159797225,6076533125,...

%e 64: 2576450045,12882250225,64411251125,167469252925,...

%e 128: 157163452745,785817263725,3929086318625,10215624428425,...

%e 256: 11472932050385,57364660251925,286823301259625,...

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

%Y Row 1 is A000351 except for starting point.

%K nonn,tabl

%O 1,2

%A _Ray Chandler_, Aug 26 2004

%E Correct offset. _Ray Chandler_, Jan 15 2013

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Last modified September 24 16:41 EDT 2022. Contains 356943 sequences. (Running on oeis4.)