OFFSET
1,2
COMMENTS
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
LINKS
Xianwen Wang, Table of n, a(n) for n = 1..5555
FORMULA
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.
EXAMPLE
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).
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul D. Hanna, Sep 12 2002
EXTENSIONS
Sequence corrected by Xianwen Wang, Feb 23 2013
STATUS
approved