Template:Sequence of the Day for October 27

Intended for: October 27, 2012

Timetable

• First draft entered by M. F. Hasler on October 27, 2011 ✓
• Draft to be reviewed by August 27, 2012
• Draft to be approved by September 27, 2012

Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.

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0
1
1 0
1 1
2 2 → 1 0 0
1 0 1
1 1 0
1 1 1
1 0 0 0
1 0 0 1
...

A105027: Write numbers in binary under each other. Starting with the first digit of each line, read diagonals upward and convert to decimal.

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

Example

After the first 4 terms resulting from the 1- and 2-binary-digit numbers, start with the initial (binary) digit of 2 2 = 1002 and read diagonal-wise upwards:

1102 = 6 = a (4)

, then starting with the first digit of 101, one reads

1012 = 5 = a (5)

, then

1002 = 4 = a (6)

and finally

1112 = 7 = a (7)

.

Comments

This is a permutation of the nonnegative integers.

The structure of the sequence is as follows: blocks of size

2 k  −  1

taken from A102370, interspersed with terms of A102371.— Philippe DELEHAM, Nov 17 2007

References

• David Applegate, Benoît Cloitre, Philippe Deléham and N. J. A. Sloane. “Sloping binary numbers: a new sequence related to the binary numbers.” J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.