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%I #2 Mar 30 2012 17:26:23
%S 1,2,3,10,4,5,6,21,7,8,9,12,11,13,14,26,15,16,17,33,18,19,20,24,22,23,
%T 25,30,27,28,29,37,31,32,34,47,35,36,38,60,39,40,41,49,42,43,44,67,45,
%U 46,48,57,50,51,52,72,53,54,55,63,56,58,59,83,61,62,64,69,65,66,68,90
%N Rearrangement of natural numbers such that each four terms sum up to a perfect square.
%e 1+2+3+10=16, 4+5+6+21=36, 7+8+9+12=36, 11+13+14+26=64.
%t s={};ra=Range[2000]; Do[su=ra[[1]]+ra[[2]]+ra[[3]]; c=4;While[ !IntegerQ[Sqrt[su+ra[[c]]]],c++ ];rac=ra[[c]]; s=Join[s,{ra[[1]],ra[[2]],ra[[3]],rac}]; ra=Complement[ra,{ra[[1]],ra[[2]],ra[[3]],rac}],{50}];s
%Y Cf. A130108, A130109, A130111.
%K nonn
%O 1,2
%A _Zak Seidov_, May 08 2007
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