%I #13 Dec 18 2020 04:26:23
%S 1,3,4,5,9,12,23,31,33,35,44,57,60,81,107,123,157,179,204,212,273,293,
%T 311,369,391,411,417,459,555,620,657,679,1076,1115,1187,1259,1275,
%U 1308,1377,1453,1713,1813,1979,2508,2604,2673,2764,2817,2885,3419,3475,3804,3849
%N Generalized Markoff numbers: union of numbers a, b, c, d, e satisfying the Markoff(5) equation a^2 + b^2 + c^2 + d^2 + e^2 = a*b*c*d*e.
%C Every term of A229240 is a term of this sequence.
%C Also, union of positive integers satisfying Hurwitz equation (x_1)^2 + (x_2)^2 + ... + (x_n)^2 = z * x_1 * x_2 * ... * x_n for z=1 and n=5.
%e {1259,35,4,3,3} is a solution and that is why 3,4,35,1259 belong to the sequence.
%t div={1,3};limit=10^4;Monitor[Do[m=div[[{a,b,c,d}]];m1=Times@@m;m2=Tr[m^2];s=Sqrt[m1^2-4m2];x1=(m1-s)/2;x2=(m1+s)/2;If[IntegerQ[x1]&&x2<limit,AppendTo[div,{x1,x2}]];div=Union@Flatten@div,{n,5},{a,l=Length@div},{b,a},{c,b},{d,c}],{"stops when",l-a,"is equal to 0"}];div
%Y Cf. A229240, A229242, A229241, A227206, A002559.
%K nonn
%O 1,2
%A _Giorgos Kalogeropoulos_, Oct 18 2020