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.

A166930 Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some positive coprime integers a, b, c.

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%I A166930 #36 Jan 11 2025 20:42:43
%S A166930 2165017,15512114571284835412957,
%T A166930 368440923990671763222767414151367493861848396861,
%U A166930 29032470413228645503712143213832535500985227130245791625262982715784415755764157625
%N A166930 Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some positive coprime integers a, b, c.
%C A166930 Square roots of the hypotenuses of Pythagorean triangles in which the hypotenuse and the sum of the legs are squares. In a letter to Mersenne in the year 1643, Fermat asserted that the smallest such triangle has the legs 4565486027761 and 1061652293520, and the hypotenuse a(1)^2 = 4687298610289.
%C A166930 Subsequence of A166929 which allows a,b be nonzero.
%C A166930 Values of m in coprime solutions to 2m^4 = c^4 + d^2 with d < c^2 (so that a,b = (c^2 +- d)/2). Corresponding values of c are given in A167438.
%D A166930 W. Sierpinski. Pythagorean Triangles. Dover Publications, 2003, ISBN 0-486-43278-5.
%H A166930 Gerry Martens, <a href="/A166930/b166930.txt">Table of n, a(n) for n = 1..13</a>
%Y A166930 Cf. A166929, A167437, A167438.
%K A166930 nonn
%O A166930 1,1
%A A166930 _Max Alekseyev_, Oct 23 2009
%E A166930 Edited by _Max Alekseyev_, Nov 03 2009