Using the i3 tiling window manager on two screens („outputs“) can be challenging. The number of workspaces grows twice as fast than with a single screen setup and it is easy to lose track of the numbers and contents of workspaces. For me personally it is more intuitive to remember a certain sequence of workspaces on each screen, which seemingly extends above and below the workspace presently displayed. (It may be that this intuition has been coined by using the GNOME Shell over extended periods.)

In order to achieve a comparable user experience within i3, I use the following Python script with the keybindings presented below. The script is inspired by an article on the i3 homepage by user captnfab. It has one dependency: ziberna/i3-py, which can be installed with pip3 install i3-py. As is apparent from the keybindings, Ctrl+Alt+Up/Down are used to switch the present workspace on the focused output. With the same keys together with +Shift you can take the focused window with you.

#!/usr/bin/python3
#
# i3-switch-workspace.py
# by Fabian Stanke
#
# Sequentially switch workspaces on present output

import i3
import argparse

parser = argparse.ArgumentParser(
    description='i3 workspace switcher.')

parser.add_argument(
    '--move', action='store_true',
    help='take the focused container with you when moving.')
parser.add_argument(
    'direction', choices=['next', 'prev'],
    help='defines in which direction to switch.')

args = parser.parse_args()

workspaces = i3.get_workspaces()

# Determine focused workspace (and thus the focused output)
focused_ws = next((w for w in workspaces if w['focused']))

# Collect all workspaces of the focused output
ws_names = list(w['name'] 
                for w in workspaces 
                if w['output'] == focused_ws['output'])

# Determine position of focused worspace in that collection
idx = ws_names.index(focused_ws['name'])
target = focused_ws['name']

if args.direction == 'next':
	# Determine next workspace	

	if (idx + 1 < len(ws_names)):
		target = ws_names[idx + 1]
	else:
		# Determine last number used on this output
		maxidx = 1
		# Determine unused numbers 
		used = {}
		for w in workspaces:
			try:
				widx = int(w['name'])
				used[widx] = True
				if w['output'] == focused_ws['output']:
					maxidx = max(widx, maxidx)
			except:
				continue
		# Increment to create new name
		while used.get(maxidx, False):
			print(maxidx)
			maxidx += 1
		target = str(maxidx)


elif args.direction == 'prev':
	# Determine previous workspace

	if (idx - 1 >= 0):
		target = ws_names[idx - 1]
	#else remain at first workspace

if args.move:
	# Move the focused container to the target workspace first
	i3.command('move', 'container to workspace ' + target)

# Switch
#print("switch to " + target)
i3.workspace(target)

My preferred keybindings to actually use the above script are:

bindsym Ctrl+Mod1+Down exec i3-switch-workspace.py next
bindsym Ctrl+Mod1+Up exec i3-switch-workspace.py prev
bindsym Ctrl+Mod1+Shift+Down exec i3-switch-workspace.py --move next
bindsym Ctrl+Mod1+Shift+Up exec i3-switch-workspace.py --move prev