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 456548602761 and 1061652293520, and the hypotenuse a(1)^2 = 4687298610289.
Subsequence of A166929 which allows a,b be nonzero.
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.
Terms 5..8 found. - Gerry Martens, Jan 15 2019