Under new regulations for 2014, Formula One drivers will have permanent racing numbers to be used throughout their careers from now on and can choose any between two and 99.
The governing International Automobile Federation (FIA) published the official list with some surprises among the selections.
Vettel, who will have the number one on his Red Bull this season, opted for the number that many fans associate with Britain's 1992 champion Nigel Mansell who was often referred to as 'Red Five'.
Venezuelan Pastor Maldonado opted to have 13, a number considered unlucky in many countries but lucky in others, on his Lotus. Traditionally the number 13 has not been used.
McLaren's Jenson Button chose to roll back the years and race with the number 22 that he used in his 2009 title-winning campaign.
"Two little ducks," the 33-year-old Briton, who won his Formula One championship with the Brawn GP team that is now Mercedes, had told his 1.6 million Twitter followers earlier. "Quack quack".
"#Jenson22 Great memories, looking forward to making a few more," he added.
In British bingo halls numbers are called out using nicknames, with 22 sometimes referred to as two little ducks or quack quack.
The question of what number drivers will choose has intrigued Formula One fans aware of the evocative past behind some of them.
The late Canadian Gilles Villeneuve, one of Ferrari's greatest heroes, remains closely identified with number 27 which was also used at times by the late Brazilian triple champion Ayrton Senna. Germany's Nico Hulkenberg will have that one.
Ferrari's Fernando Alonso requested 14, which he explained last month has been his lucky number since 1996 when at the age of 14 he won a karting title with 14 on his car on July 14.
"Let's see if it's lucky for me again," he told reporters in Madrid.
The Spaniard is also a fan of the Real Madrid soccer club, whose Spain international midfielder Xabi Alonso plays with the number 14 shirt.
Alonso's new Finnish team mate, and 2007 world champion, Kimi Raikkonen has opted for seven while 2008 champion Lewis Hamilton took 44. Germany's Adrian Sutil, who has joined Sauber from Force India, chose 99.
Daniel Ricciardo, who has joined Vettel at Red Bull, will race as number three.
Previously, the smiling Australian would have had to have the number two on his car as the champion's team mate - a status very few racing drivers willingly accept and none chose.
Numbers of confirmed drivers (in 2013 constructors' championship order):
1 (as champion) or 5 - Sebastian Vettel (Germany) Red Bull
3 - Daniel Ricciardo (Australia) Red Bull
44 - Lewis Hamilton (Britain) Mercedes
6 - Nico Rosberg (Germany) Mercedes
14 - Fernando Alonso (Spain) Ferrari
7 - Kimi Raikkonen (Finland) Ferrari
8 - Romain Grosjean (France) Lotus
13 - Pastor Maldonado (Venezuela) Lotus
22 - Jenson Button (Britain) McLaren
20 - Kevin Magnussen (Denmark) McLaren
27 - Nico Hulkenberg (Germany) Force India
11 - Sergio Perez (Mexico) Force India
99 - Adrian Sutil (Germany) Sauber
21 - Esteban Gutierrez (Mexico) Sauber
25 - Jean-Eric Vergne (France) Toro Rosso
26 - Daniil Kvyat (Russia) Toro Rosso
19 - Felipe Massa (Brazil) Williams
77 - Valtteri Bottas (Finland) Williams
17 - Jules Bianchi (France) Marussia