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A183169
Tree generated by the squares.
3
1, 2, 4, 3, 16, 6, 9, 5, 256, 20, 36, 8, 81, 12, 25, 7, 65536, 272, 400, 24, 1296, 42, 64, 11, 6561, 90, 144, 15, 625, 30, 49, 10, 4294967296, 65792, 73984, 288, 160000, 420, 576, 29, 1679616, 1332, 1764, 48, 4096, 72, 121, 14
OFFSET
1,2
COMMENTS
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.
FORMULA
Let L(n) be the n-th square (A000290).
Let U(n) be the n-th nonsquare (A000037).
The tree-array T(n,k) is then given by rows:
T(0,0)=1; T(1,0)=2;
T(n,2j)=L(T(n-1),j);
T(n,2j+1)=U(T(n-1),j);
for j=0,1,...,2^(n-1)-1, n>=2.
EXAMPLE
First levels of the tree:
......................1
......................2
...........4.....................3
.......16.......6...........9..........5
...256...20...36..8......81...12....25...7
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Dec 28 2010
STATUS
approved