A198468 -id:A198468 - cp's OEIS frontend

A198457 Consider triples (a, b, c) where a <= b < c and (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives a, b and c values in that order.

3, 6, 7, 4, 4, 6, 5, 16, 17, 6, 10, 12, 7, 8, 11, 7, 30, 31, 8, 18, 20, 9, 14, 17, 9, 48, 49, 10, 12, 16, 10, 28, 30, 11, 70, 71, 12, 18, 22, 12, 40, 42, 13, 16, 21, 13, 30, 33, 13, 96, 97, 14, 25, 29, 14, 54, 56, 15, 22, 27, 15, 40, 43, 15, 126, 127, 16, 20, 26

Offset: 1

Charlie Marion, Nov 09 2011

See A198453.

Because either all sides or only one side of a Pythagorean (-+2)-triangle ABC is even their sum is always even. Thus csc(C) = -(a+b+c+k)/k is an integer. So ((a+2)^2 + (b+2)^2 - (c+2)^2)|(2*(a+2)*(b+2)) resp. (a^2 + b^2 - c^2)|(2*a*b). - Ralf Steiner, Sep 18 2019

			3*5 +  6*8  =  7*9;
4*6 +  4*6  =  6*8;
5*7 + 16*17 = 17*18;
6*8 + 10*12 = 12*14;
7*9 +  8*10 = 11*13;
7*9 + 30*32 = 31*33.

A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

David A. Corneth, Table of n, a(n) for n = 1..9999
Ron Knott, Pythagorean Triples and Online Calculators.

Cf. A103606, A198453-A198456, A198458-A198468.

More terms from David A. Corneth, Sep 22 2019

cp's OEIS Frontend

A198457 Consider triples (a, b, c) where a <= b < c and (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives a, b and c values in that order.

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