A183169 Tree generated by the squares.

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

Author

Clark Kimberling, Dec 28 2010

Keywords

• nonn
• tabf

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.

Examples

			First levels of the tree:
......................1
......................2
...........4.....................3
.......16.......6...........9..........5
...256...20...36..8......81...12....25...7
		

Crossrefs

Cf. A183079, A000037, A183169, A001146, 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.