How to create weird bitcoin addresses?

[Fellane]

I am pretty sure almost everyone seen such addresses:

1BitcoinEaterAddressDontSendf59kuE
1111111111111111111114oLvT2
1CounterpartyXXXXXXXXXXXXXXXUWLpVr
1xxxxxxxxxxxxxxxxxxxxxxxxxy1kmdGr
1of1xxxxx1anonymity1xxxxxxxz9JzFN
1topic1xxx1hmwyda1xxxxxxxxxvo8wMn

And there is a lot more of them. I also know that there is no private keys for these addresses and bitcoins sent to these addresses will be lost forever.
So my question is: How can I create valid bitcoin address with specified pattern which could be checked in blockchain. Is there any step by step guide how to do that?

[hosseinimr93]

Read the topic created by 1miau.

[Guide] How to create your customized Bitcoin-Address (vanitygen) – step by step

[Fellane]

Read the topic created by 1miau.

[Guide] How to create your customized Bitcoin-Address (vanitygen) – step by step

Please, read the topic again. There is nothing about vanitygen in my question. Weird bitcoin addresses I mentioned were created not with vanitygen. Or maybe they were, idk. But link that you sent - there is nothing helpful to cover my topic.

[nc50lc]

There are a couple of online "Proof of Burn" address generators out there like this one: https://gobittest.appspot.com/ProofOfBurn
It only supports legacy Bitcoin address and you'll likely encounter problems with max number of prefix.

Example of a valid weird address: 3HeyThisisAProofofBurnAddressxrgL7
It's a P2SH address and made using a python tool created by someone else but I can't find the download link.
-Edit-
Found it: https://gist.github.com/CoinWhisperer/6d673f1f3d13da1611cd
Read the comments for the dependencies.

[pooya87]

Is there any step by step guide how to do that?

1. start with 1 or 3
2. write between 19 (26-6-1) and 28 (35-6-1) characters (-1 is for initial char, -6 is for checksum)
3. check if any of the characters are 0OIl and change them.
4. add 6 arbitrary characters (like 1) at the end.
5. decode using base58 encoding
6. make sure the data length is 25 (1+20+4) and first byte is 0 or 5 depending on step #1
7. use bytes 0 to 20 (the first 21 bytes) as the actual data
8. encode using base58check (with a checksum)
9. don't use this address, use OP_RETURN to burn coins. it can also contain messages that are a lot longer than 20 bytes the address can hold.

[khaled0111]

And there is a lot more of them. I also know that there is no private keys for these addresses and bitcoins sent to these addresses will be lost forever.

Those weird addresses are called burn addresses. The coins sent to them are lost not because they don't have private keys, as you believe, but because there is no way to derive those private keys (which are needed to spend).
When you want to create a bitcoin address, you start by generating a private key then you derive the public address from it through a one way functions.
You can create a valid address directly as pooya87 explained above but you can't go the other way around to get its private key.

[Chikito]

Here you go How did this address come into being 1BitcoinEaterAddressDontSendf59kuE?

[ABCbits]

Read the topic created by 1miau.

[Guide] How to create your customized Bitcoin-Address (vanitygen) – step by step

Vanity address generator aren't capable to generate address with so many prefix