A379506
Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its inradius the semiperimeter of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.
Original entry on oeis.org
3, 4, 5, 13, 84, 85, 183, 16744, 16745, 33673, 566935464, 566935465, 1133904603, 642869824352293804, 642869824352293805, 1285739649838492213, 826563223583404284483387832630818684, 826563223583404284483387832630818685
Offset: 1
Triples begin:
3, 4, 5;
13, 84, 85;
183, 16744, 16745;
33673, 566935464, 566935465;
-
{a0,b0,c0}={3,4,5};f[n_]:= Module[{fn0=a0+b0+c0+1,fn1=((a0+b0+c0+1)^2+1)/2},Do[{fn0,fn1}={2fn1+fn0,((2fn1+fn0)^2+1)/2},{n}];fn0];t[n_]:={f[n-1],(f[n-1]^2-1)/2,(f[n 1]^2+1)/2};ternas={a0,b0,c0};For[i=1,i<=6,i++,ternas=Join[ternas,t[i]]];ternas
A378963
Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its inradius the short leg of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.
Original entry on oeis.org
3, 4, 5, 7, 24, 25, 15, 112, 113, 31, 480, 481, 63, 1984, 1985, 127, 8064, 8065, 255, 32512, 32513, 511, 130560, 130561, 1023, 523264, 523265, 2047, 2095104, 2095105, 4095, 8384512, 8384513, 8191, 33546240, 33546241, 16383, 134201344, 134201345
Offset: 1
Triples begin:
3, 4, 5;
7, 24, 25;
15, 112, 113;
31, 480, 481;
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz, and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
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a=Table[2^(n+1)-1,{n,1,13}];Apply[Join,Map[{#,(#^2-1)/2,(#^2+1)/2}&,a]]
A380299
Sequence of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its inradius the area of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.
Original entry on oeis.org
3, 4, 5, 13, 84, 85, 1093, 597324, 597325, 652875133, 213122969644883844, 213122969644883845, 139142687152258502421051253, 9680343693975641657052402486887446135645084826435004, 9680343693975641657052402486887446135645084826435005
Offset: 1
Triples begin:
3, 4, 5;
13, 84, 85;
1093, 597324, 597325;
652875133, 213122969644883844, 213122969644883845;
- El Libro de las Ternas Pitagóricas, Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz y José Miguel Blanco Casado, Preprint, 2025.
-
{a0,b0,c0}={3,4,5};f[n_]:=Module[{fn0=a0 b0+1,fn1=((a0 b0+1)^2-1)/2},Do[{fn0,fn1}={fn1 fn0+1,((fn1 fn0+1)^2-1)/2},{n}];fn0];t[n_]:= {f[n-1],(f[n-1]^2-1)/2,(f[n-1]^2+1)/2};ternas={a0,b0,c0};For[i=1,i<=5,i++,ternas=Join[ternas,t[i]]];ternas
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