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%I #7 Jul 12 2012 00:39:52
%S 1,2,4,3,16,6,9,5,256,20,36,8,81,12,25,7,65536,272,400,24,1296,42,64,
%T 11,6561,90,144,15,625,30,49,10,4294967296,65792,73984,288,160000,420,
%U 576,29,1679616,1332,1764,48,4096,72,121,14
%N Tree generated by the squares.
%C A permutation of the positive integers. See the comment at A183079 (tree generated by the triangular numbers). The leftmost numbers (1,2,4,16,...) are, after the initial 1, given by A001146. The rightmost numbers (1,2,3,5,7,10,...) are, after the initial 1, the iterates of the nonsquare function; see a comment at A033638.
%F Let L(n) be the n-th square (A000290).
%F Let U(n) be the n-th nonsquare (A000037).
%F The tree-array T(n,k) is then given by rows:
%F T(0,0)=1; T(1,0)=2;
%F T(n,2j)=L(T(n-1),j);
%F T(n,2j+1)=U(T(n-1),j);
%F for j=0,1,...,2^(n-1)-1, n>=2.
%e First levels of the tree:
%e ......................1
%e ......................2
%e ...........4.....................3
%e .......16.......6...........9..........5
%e ...256...20...36..8......81...12....25...7
%Y Cf. A183079, A000037, A183169, A001146, A033638.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Dec 28 2010
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