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%I #15 Dec 17 2013 14:12:29
%S 1,4,9,16,36,64,144,256,289,576,1024,1156,2304,4096,4624,9216,16384,
%T 18496,36864,65536,73984,147456,262144,295936,589824,1048576,1183744,
%U 2359296,4194304,4734976,9437184,16777216,18939904,37748736,67108864,75759616,150994944
%N Lexicographically least sequence of squares that are sum-free.
%C A sum-free sequence has no term that is the sum of a subset of its previous terms. There are an infinite number of sequences that are subsets of the squares and sum-free. This sequence is lexicographically the first.
%H H. L. Abbott, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa48/aa4819.pdf">On sum-free sequences</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/A-Sequence.html">MathWorld: A-Sequence</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sum-free_sequence">Sum-free sequence</a>
%F Conjecture: a(n) = 4*a(n-3) for n>9. G.f.: -x*(33*x^8 +112*x^7 +80*x^6 +28*x^5 +20*x^4 +12*x^3 +9*x^2 +4*x +1) / (4*x^3 -1). - _Colin Barker_, May 28 2013
%e a(10)=576 as 576 is the next square after a(9)=289 that cannot be formed from distinct sums of a(1),...,a(9) (1,4,9,16,36,64,144,256,289).
%t memberQ[n1_, k1_] := If[Select[IntegerPartitions[n1^2, Length[k1], k1], Sort@#==Union@# &]=={}, False, True]; k={1}; n=1; While[Length[k]<20, (If[!memberQ[n, k], k=Append[k, n^2]]; n++)]; k
%Y Cf. A225947.
%K nonn
%O 1,2
%A _Frank M Jackson_, May 25 2013
%E More terms from _Colin Barker_, May 28 2013
%E a(33)-a(37) from _Donovan Johnson_, Dec 17 2013
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