%I #47 Feb 05 2014 20:59:23
%S 1,3,11,41,131,153,571,1561,1803,2131,5761,7953,17291,18601,25091,
%T 29681,79291,110771,221651,253353,295681,349451,413403,817961,1542841,
%U 2282281,2453891,2641211,3018753,3252611,3487001,4114771,4867203,5757961,11141771
%N Generalized Markoff numbers: union of numbers a, b, c, d satisfying the Markoff(4) equation a^2 + b^2 + c^2 + d^2 = 4*a*b*c*d.
%C a,b,c,d is a solution to a^2 + b^2 + c^2 + d^2 = 4*a*b*c*d if and only if 2a, 2b, 2c, 2d is a solution to a^2 + b^2 + c^2 + d^2 = a*b*c*d. - _Shanzhen Gao_, Sep 18 2013
%H Xianwen Wang, <a href="/A075276/b075276.txt">Table of n, a(n) for n = 1..5555</a>
%F If (a, b, c, d) satisfies Markoff(4) equation, then so does (a, b, c, 4abc - d) and 4abc - d = (a^2 + b^2 + c^2)/d.
%e Some solutions to Markoff(4) equation a^2 + b^2 + c^2 + d^2 = 4abcd are (1,1,1,1), (1,1,1,3), (1,1,3,11), (1,3,11,131), (3,11,131,17291), (1,1,11,41), (1,11,41,1803), (1,1,41,153), (1,3,131,1561), (1,11,131,5761), (1,1,153,571), (1,1,571,2131), (1,1,2131,7953), (1,3,1561,18601).
%t MAX=10^10; data = NestWhile[Select[Union[Sort/@Flatten[Table[{a,b,c,4 a b c-d}/.MapThread[Rule,{{a,b,c,d},#}]&/@Map[RotateLeft[ii,#]&,Range[4]],{ii,#}],1]], Max[#] < MAX&]&,{{1,1,1,1},{1,1,1,3}}, UnsameQ,2]; Take[data//Flatten//Union, 30] (* _Xianwen Wang_, Feb 23 2013 *)
%Y Cf. A002559.
%K easy,nonn
%O 1,2
%A _Paul D. Hanna_, Sep 12 2002
%E Sequence corrected by _Xianwen Wang_, Feb 23 2013