May near seeds in random number generation give similar random numbers?
To quote the documentation from the random module:

General notes on the underlying Mersenne Twister core generator:

The period is 2**19937-1.
It is one of the most extensively tested generators in existence.


I'd be more worried about my code being broken than my RNG not being random enough.  In general, your gut feelings about randomness are going to be wrong - the Human mind is really good at finding patterns, even if they don't exist.
As long as you know your results aren't going to be 'secure' due to your lack of random seeding, you should be fine.
I'm using sequential seeds (1,2,3,4,...) for generation of random numbers in a simulation. Does the fact that the seeds are near each other make the generated pseudo-random numbers similar as well?
I think it doesn't change anything, but I'm using python
Edit: I have done some tests and the numbers don't look similar. But I'm afraid that the similarity cannot be noticed just by looking at the numbers. Is there any theoretical feature of random number generation that guarantees that different seeds give completely independent pseudo-random numbers?