A089552 -id:A089552 - cp's OEIS frontend

A089548 Long leg of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

40, 156, 340, 561, 1173, 1624, 1581, 3577, 3816, 3901, 5460, 7029, 7480, 9636, 8544, 9717, 12513, 17460, 17004, 13000, 20701, 20349, 18601, 32361, 32880, 26329, 34540, 29869, 37909, 48357, 46320, 41820, 50320, 56784, 47817, 64893, 69649, 60580

Offset: 1

Ray Chandler, Nov 16 2003

nonn

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A088319, A088515, A088516, A088546, A089545-A089552, A089554-A089558.

A089555 a(n)=A088516(n)/2.

Original entry on oeis.org

2, 3, 1, 4, 1, 2, 5, 6, 2, 1, 7, 7, 2, 3, 8, 1, 8, 9, 3, 2, 9, 1, 10, 10, 4, 2, 11, 11, 1, 11, 12, 3, 4, 12, 2, 1, 12, 13, 13, 13, 4, 3, 5, 2, 14, 13, 1, 14, 4, 5, 15, 14, 2, 1, 16, 16, 5, 16, 4, 15, 6, 3, 16, 2, 17, 17, 17, 16, 1, 17, 6, 4, 18, 7, 3, 18, 2, 17, 19, 19, 5, 1, 4, 7, 19, 19, 18, 19

Offset: 1

Ray Chandler, Nov 16 2003

nonn

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A088319, A088515, A088516, A088546, A089545-A089552, A089554-A089558.

A089557 a(n) = A089546(n)/2.

Original entry on oeis.org

2, 3, 5, 4, 7, 14, 5, 6, 18, 9, 21, 7, 22, 33, 24, 11, 8, 45, 39, 26, 9, 13, 30, 10, 60, 30, 55, 33, 15, 11, 60, 51, 68, 84, 34, 17, 12, 65, 91, 39, 76, 57, 95, 38, 70, 13, 19, 42, 84, 105, 105, 14, 42, 21, 112, 80, 115, 144, 92, 15, 138, 69, 48, 46, 119, 85, 153, 16, 23, 51, 150

Offset: 1

Ray Chandler, Nov 16 2003

nonn

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A088319, A088515, A088516, A088546, A089545-A089552, A089554-A089558.

A145906 Concerning hypotenuses of triangles such that the sum of the two legs is a perfect square.

Original entry on oeis.org

9, 19, 27, 33, 57, 51, 51, 73, 89, 83, 107, 99, 139, 129, 137, 123, 129, 187, 187, 163, 177, 171, 209, 257, 201, 233, 267, 227, 251, 337, 243, 321, 313, 307, 297, 289, 291, 387, 411, 363, 347, 393, 339, 379, 369, 363, 417, 401, 393, 491, 499, 473, 593, 449

Offset: 0

Paul Curtz, Oct 23 2008

Last digit is never 5.
Frenicle considers numbers N (apparently the set of A058529 or A120681) and their squares N^2. These have representations N=2*b^2-a^2 = d^2-2*c^2 with d=b+c and N^2 = 2*f^2-e^2 = h^2-2*g^2 with h=f+g. For example N=7 with a=1, b=2, c=1, d=3 and N^2=49 with e=1, f=5, g=4, h=9. The current sequence contains the list of h's.
Apparently the list of N^2 is A089552, the list of a in A143732, the list of b in A147847, the list of e (in different order) in A152910, the list of f (sorted into a different order) in A020882.

			(a,b,c,d,e,f,g,h) = (1,2,1,3,1,5,4,9) with N=7 or  (1,3,2,5,7,13,6,19) with N=17 or (3,4,1,5,7,17,10,27) with N=23 or (1,4,3,7,17,25,8,33) with N=31.

M. de Frenicle, Methode pour trouver la solutions des problemes par les exclusions, in: Divers ouvrages des mathematiques et de physique par messieurs de l'academie royale des sciences, (1693) pp 1-44.

Cf. A144407

A089549 Semiperimeter of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

Original entry on oeis.org

45, 247, 459, 825, 1887, 1653, 2091, 4453, 4717, 5395, 6955, 8415, 10965, 10147, 12193, 12423, 14577, 18139, 20383, 22125, 23635, 24795, 31141, 36381, 35209, 40309, 41919, 46435, 44719, 53703, 60409, 62935, 59385, 56953, 68013, 74787

Offset: 1

Ray Chandler, Nov 16 2003

nonn

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A088319, A088515, A088516, A088546, A089545-A089552, A089554-A089558.

A089550 One sixth area of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

Original entry on oeis.org

30, 1729, 5355, 18700, 101269, 7714, 108035, 436394, 481134, 760695, 1119755, 1394085, 3296810, 781319, 3999304, 3598529, 3770584, 1904595, 8214349, 13997750, 9004935, 12785955, 27715490, 19524470, 11971060, 45549170, 36120205

Offset: 1

Ray Chandler, Nov 16 2003

nonn

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A088319, A088515, A088516, A088546, A089545-A089552, A089554-A089558.

A089556 a(n)=(A089545(n)+1)/2.

Original entry on oeis.org

3, 7, 9, 13, 19, 15, 21, 31, 27, 33, 33, 43, 43, 37, 45, 51, 57, 49, 55, 63, 73, 73, 75, 91, 69, 87, 79, 93, 99, 111, 97, 103, 93, 85, 115, 129, 133, 117, 103, 135, 121, 133, 111, 147, 139, 157, 163, 159, 153, 141, 145, 183, 183, 201, 169, 189, 175, 153, 189, 211

Offset: 1

Ray Chandler, Nov 16 2003

nonn

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A088319, A088515, A088516, A088546, A089545-A089552, A089554-A089558.

cp's OEIS Frontend

A089548 Long leg of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

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A089555 a(n)=A088516(n)/2.

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A089557 a(n) = A089546(n)/2.

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A145906 Concerning hypotenuses of triangles such that the sum of the two legs is a perfect square.

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A089549 Semiperimeter of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

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Keywords

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A089550 One sixth area of primitive Pythagorean triangles having legs that add up to a square, sorted on hypotenuse.

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A089556 a(n)=(A089545(n)+1)/2.

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