A340958 Concatenated layouts of page numbers as in a printed bound booklet with 2 pages per side with 0's representing blanks.

0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 2, 3, 4, 1, 2, 3, 0, 1, 2, 0, 0, 3, 4, 5, 0, 1, 2, 0, 6, 3, 4, 5, 0, 1, 2, 7, 6, 3, 4, 5, 8, 1, 2, 7, 6, 3, 4, 5, 0, 1, 2, 0, 0, 3, 4, 9, 8, 5, 6, 7, 0, 1, 2, 0, 10, 3, 4, 9, 8, 5, 6, 7, 0, 1, 2, 11, 10, 3, 4, 9, 8, 5, 6, 7

Offset

1,7

Comments

The contents of each piece of paper are represented by 4 integers: the 1st is the outside left page number (or 0 for blank); the 2nd is outside right, 3rd inside left, and 4th inside right. Assumes left-to-right writing direction on paper in landscape orientation.

Links

Table of n, a(n) for n=1..84.

Adobe Inc., Diagram showing the layout of a booklet print-out

Patrick Reader, The Printer Booklet Sequence, Code Golf Stack Exchange.

Example

      |   Page numbers   |
      | (or 0 for blank) |
Piece +---------+--------+
  of  | Outside | Inside |
paper |   L  R  |  L  R  |
------+---------+--------+---------------
   1  |   0  1  |  0  0  | 1-page booklet
------+---------+--------+---------------
   2  |   0  1  |  2  0  | 2-page booklet
------+---------+--------+---------------
   3  |   0  1  |  2  3  | 3-page booklet
------+---------+--------+---------------
   4  |   4  1  |  2  3  | 4-page booklet
------+---------+--------+---------------
   5  |   0  1  |  2  0  | 5-page
   6  |   0  3  |  4  5  | booklet
------+---------+--------+---------------
   7  |   0  1  |  2  0  | 6-page
   8  |   6  3  |  4  5  | booklet
------+---------+--------+---------------
   9  |   0  1  |  2  7  | 7-page
  10  |   6  3  |  4  5  | booklet
------+---------+--------+---------------
  11  |   8  1  |  2  7  | 8-page
  12  |   6  3  |  4  5  | booklet
------+---------+--------+---------------
  13  |   0  1  |  2  0  | 9-page
  14  |   0  3  |  4  9  | booklet
  15  |   8  5  |  6  7  |
------+---------+--------+---------------
  16  |   0  1  |  2  0  | 10-page
  17  |  10  3  |  4  9  | booklet
  18  |   8  5  |  6  7  |
------+---------+--------+---------------
  19  |   0  1  |  2 11  | 11-page
  20  |  10  3  |  4  9  | booklet
  21  |   8  5  |  6  7  |

Prog

(Python)
from math import ceil
def sequence():
    p = 0
    while True:
        p += 1
        a = [0] * 4 * ceil(p / 4)
        g = len(a) // 4
        n = 1
        for i in range(g):
            a[i * 4 + 1] = n
            n += 1
            if n > p: break
            a[i * 4 + 2] = n
            n += 1
        for i in reversed(range(g)):
            if n > p: break
            a[i * 4 + 3] = n
            n += 1
            if n > p: break
            a[i * 4] = n
            n += 1
        yield from a

Crossrefs

Sequence in context: A263141 A051510 A361800 * A320781 A284608 A325201

Adjacent sequences: A340955 A340956 A340957 * A340959 A340960 A340961

Keyword

nonn,tabf,easy

Author

Patrick Reader, Apr 25 2021

Status

approved