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Largest number in an integer 6-tuple (a, b, c, d, e, f) satisfying the Markoff(6) equation a^2+b^2+c^2+d^2+e^2+f^2 = 6*a*b*c*d*e*f.
1

%I #11 Oct 04 2013 13:15:15

%S 1,5,29,169,869,985,5741,26041,29405,33461,151201,195025,756029,

%T 780361,998789,1136689,5116301,6625109,23384789,26308105,29816641,

%U 33929309,38613965,135777769,225058681,657744361,678888869,700763309,788361985,864683429,890206969,1012771061,1152597605

%N Largest number in an integer 6-tuple (a, b, c, d, e, f) satisfying the Markoff(6) equation a^2+b^2+c^2+d^2+e^2+f^2 = 6*a*b*c*d*e*f.

%C 2*a(n)^2-1 is a square for a(1), a(2), a(3), a(4), a(6), a(7), a(10), a(12), a(16), a(18), a(23), a(25),...

%e 1 is in the sequence since (1, 1, 1, 1, 1, 1) is a solution to a^2+b^2+c^2+d^2+e^2+f^2 = 6*a*b*c*d*e*f. 5, 29, and 169 are in the sequence since (5, 1, 1, 1, 1, 1), (29, 5, 1, 1, 1, 1), (169, 29, 1, 1, 1, 1) are solutions.

%Y Cf. A001653, A229242 (Markoff(5)).

%K nonn

%O 1,2

%A _Shanzhen Gao_, Sep 18 2013