cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A253803 a(n) gives one fourth of the even leg of one of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253802(n).

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%I A253803 #10 Jan 10 2017 05:01:59
%S A253803 6,39,60,210,210,410,630,915,1320,1780,2340,990,2730,3164,4620,5215,
%T A253803 5610,4290,8145,8106,2730,6630,12116,12540,4080,17485,17451,18480,
%U A253803 9690,24414
%N A253803 a(n) gives one fourth of the even leg of one of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253802(n).
%C A253803 See A253802 for comments and the Dickson reference.
%D A253803 L. E. Dickson, History of the Theory of Numbers, Carnegie Institution, Publ. No. 256, Vol. II, Washington D.C., 1920, p. 227.
%F A253803 a(n) = sqrt(A080109(n)^2 - A253802(n)^2)/4, n >= 1.
%e A253803 n = 7: A080175(7) = 7890481 = 53^4 = 2809^2; A002144(7)^4 = A253802(7)^2 + (4*a(7))^2 = 1241^2 + (4*630)^2.
%e A253803 The other Pythagorean triangle with hypotenuse
%e A253803 53^2 = 2809 has odd leg A253804(7) = 2385 and even leg 4*A253305(7) = 4*371 = 1484: 53^4 = 2385^2 + (4*371)^2.
%Y A253803 Cf. A002144, A080109, A253802, A253804, A253805.
%K A253803 nonn,easy
%O A253803 1,1
%A A253803 _Wolfdieter Lang_, Jan 14 2015