Template:Sequence of the Day for October 23

Intended for: October 23, 2011

Timetable

• Draft entered by Daniel Forgues on October 23, 2012 ✓
• Draft reviewed by Daniel Forgues on October 22, 2015 ✓
• Draft to be approved by September 23, 2011

Yesterday's SOTD * Tomorrow's SOTD

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A105027 Write numbers in binary under each other; to get the next block of

2 k, k   ≥   0,

terms of the sequence, start at

2 k

, read diagonals in upward direction and convert to decimal.

{ 0, 1, 3, 2, 6, 5, 4, 7, ... }

This is a permutation of the nonnegative integers (and for

n > 0

, a permutation of the positive integers). Furthermore, for each block of numbers with

k

binary digits, we have a permutation of this block.

 ........0
 ........1
 ......1 0    <- Starting here, the upward diagonals
 ......1 1       read 11, 10, giving the block 3, 2. 
 ....1 0 0    <- Starting here, the upward diagonals
 ....1 0 1       read 110, 101, 100, 111, giving the block 6, 5, 4, 7. 
 ....1 1 0       
 ....1 1 1
 ..1 0 0 0    
 ..1 0 0 1    
 ..1 0 1 0
 ..1 0 1 1
 ..1 1 0 0
 ..1 1 0 1
 ..1 1 1 0
 ..1 1 1 1