A269752 Table of inverse permutations of the rows of A131987: Position of numbers inserted in "storage order" into a perfect binary table of 2^k-1 nodes.

1, 2, 1, 3, 4, 2, 6, 1, 3, 5, 7, 8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15, 16, 8, 24, 4, 12, 20, 28, 2, 6, 10, 14, 18, 22, 26, 30, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 16, 48, 8, 24, 40, 56, 4, 12, 20, 28, 36, 44, 52, 60, 2

Offset: 1

Author

M. F. Hasler, Mar 04 2016

Keywords

• nonn
• tabf

Comments

Row n is the permutation of {1,...,2^n-1} which is the inverse of row n of A131987. See example for an illustration.

Examples

			Row 4 of A131987 is obtained by reading the following binary tree, filled with numbers {1,...,15} in "storage order", from the leftmost to the rightmost number:
       _____1_____
    __2__       __3__
   4     5     6     7
  8 9  10 11 12 13 14 15
This yields the sequence p = (8, 4, 9, 2, 10, 5, 11, 1, 12, 6, 13, 3, 14, 7, 15) which is a permutation of (1, ..., 15). Row 4 of the present table yields the inverse permutation p' = (8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15), where p'(i) is the index of i in p, e.g. p'(3)=12 because 3 = p(12).
		

Programs

PARI

A269752_row(n)=Vec(vecsort(A131987_row(n),,1))