Random.org (https://random.org) direct links for generating roulette number sequences.
European:
37 spins (one cycle)
https://www.random.org/integers/?num=37&min=0&max=36&col=1&base=10&format=plain&rnd=new
74 spins (two cycles)
https://www.random.org/integers/?num=74&min=0&max=36&col=1&base=10&format=plain&rnd=new
100 spins
https://www.random.org/integers/?num=100&min=0&max=36&col=1&base=10&format=plain&rnd=new
111 spins (three cycles)
https://www.random.org/integers/?num=111&min=0&max=36&col=1&base=10&format=plain&rnd=new
200 spins
https://www.random.org/integers/?num=200&min=0&max=36&col=1&base=10&format=plain&rnd=new
300 spins
https://www.random.org/integers/?num=300&min=0&max=36&col=1&base=10&format=plain&rnd=new
400 spins
https://www.random.org/integers/?num=400&min=0&max=36&col=1&base=10&format=plain&rnd=new
500 spins
https://www.random.org/integers/?num=500&min=0&max=36&col=1&base=10&format=plain&rnd=new
600 spins
https://www.random.org/integers/?num=600&min=0&max=36&col=1&base=10&format=plain&rnd=new
700 spins
https://www.random.org/integers/?num=700&min=0&max=36&col=1&base=10&format=plain&rnd=new
800 spins
https://www.random.org/integers/?num=800&min=0&max=36&col=1&base=10&format=plain&rnd=new
900 spins
https://www.random.org/integers/?num=900&min=0&max=36&col=1&base=10&format=plain&rnd=new
1,000 spins
https://www.random.org/integers/?num=1000&min=0&max=36&col=1&base=10&format=plain&rnd=new
2,000 spins
https://www.random.org/integers/?num=2000&min=0&max=36&col=1&base=10&format=plain&rnd=new
3,000 spins
https://www.random.org/integers/?num=3000&min=0&max=36&col=1&base=10&format=plain&rnd=new
4,000 spins
https://www.random.org/integers/?num=4000&min=0&max=36&col=1&base=10&format=plain&rnd=new
5,000 spins
https://www.random.org/integers/?num=5000&min=0&max=36&col=1&base=10&format=plain&rnd=new
6,000 spins
https://www.random.org/integers/?num=6000&min=0&max=36&col=1&base=10&format=plain&rnd=new
7,000 spins
https://www.random.org/integers/?num=7000&min=0&max=36&col=1&base=10&format=plain&rnd=new
8,000 spins
https://www.random.org/integers/?num=8000&min=0&max=36&col=1&base=10&format=plain&rnd=new
9,000 spins
https://www.random.org/integers/?num=9000&min=0&max=36&col=1&base=10&format=plain&rnd=new
10,000 spins
https://www.random.org/integers/?num=10000&min=0&max=36&col=1&base=10&format=plain&rnd=new
American*:
38 spins (one cycle)
https://www.random.org/integers/?num=38&min=0&max=37&col=1&base=10&format=plain&rnd=new
76 spins (two cycles)
https://www.random.org/integers/?num=76&min=0&max=37&col=1&base=10&format=plain&rnd=new
100 spins
https://www.random.org/integers/?num=100&min=0&max=37&col=1&base=10&format=plain&rnd=new
114 spins (three cycles)
https://www.random.org/integers/?num=114&min=0&max=37&col=1&base=10&format=plain&rnd=new
200 spins
https://www.random.org/integers/?num=200&min=0&max=37&col=1&base=10&format=plain&rnd=new
300 spins
https://www.random.org/integers/?num=300&min=0&max=37&col=1&base=10&format=plain&rnd=new
400 spins
https://www.random.org/integers/?num=400&min=0&max=37&col=1&base=10&format=plain&rnd=new
500 spins
https://www.random.org/integers/?num=500&min=0&max=37&col=1&base=10&format=plain&rnd=new
600 spins
https://www.random.org/integers/?num=600&min=0&max=37&col=1&base=10&format=plain&rnd=new
700 spins
https://www.random.org/integers/?num=700&min=0&max=37&col=1&base=10&format=plain&rnd=new
800 spins
https://www.random.org/integers/?num=800&min=0&max=37&col=1&base=10&format=plain&rnd=new
900 spins
https://www.random.org/integers/?num=900&min=0&max=37&col=1&base=10&format=plain&rnd=new
1,000 spins
https://www.random.org/integers/?num=1000&min=0&max=37&col=1&base=10&format=plain&rnd=new
2,000 spins
https://www.random.org/integers/?num=2000&min=0&max=37&col=1&base=10&format=plain&rnd=new
3,000 spins
https://www.random.org/integers/?num=3000&min=0&max=37&col=1&base=10&format=plain&rnd=new
4,000 spins
https://www.random.org/integers/?num=4000&min=0&max=37&col=1&base=10&format=plain&rnd=new
5,000 spins
https://www.random.org/integers/?num=5000&min=0&max=37&col=1&base=10&format=plain&rnd=new
6,000 spins
https://www.random.org/integers/?num=6000&min=0&max=37&col=1&base=10&format=plain&rnd=new
7,000 spins
https://www.random.org/integers/?num=7000&min=0&max=37&col=1&base=10&format=plain&rnd=new
8,000 spins
https://www.random.org/integers/?num=8000&min=0&max=37&col=1&base=10&format=plain&rnd=new
9,000 spins
https://www.random.org/integers/?num=9000&min=0&max=37&col=1&base=10&format=plain&rnd=new
10,000 spins
https://www.random.org/integers/?num=10000&min=0&max=37&col=1&base=10&format=plain&rnd=new
*: 00 is represented by 37.