I don't see any technically reason as to why you can't search through addresses generated by an HD wallet looking for a desired vanity address and/or "sequence". However, given how many addresses one generally needs to generate to find desired vanity addresses, you'll probably find that your derivation paths for the individual addresses will have outrageous gaps in them:
For instance:
bc1qxx1xxx m/44'/0'/0'/435433
bc1qxx2xxx m/44'/0'/0'/357234931
etc etc... This would make restoring from the HD wallet seed ridiculously difficult unless you had some way to track the individual derivation paths. You might even find that the "next" address in the "sequence" was actually generated previously in a "lower" derivation path value...
I doubt you'll ever find such a sequence where derivation paths are also in sequence (While I'd guess the probability of such a sequence existing is non-zero, I'd also guess it was very very very small
![Tongue](https://bitcointalk.org/Smileys/default/tongue.gif)
)
So, I'd think it would be less hassle (both in generating and restoring) to simply find the individual addresses you're after the "normal" way (eg. VanityGen)... and then import those individual private keys into the wallet of your choice.
Convincing the wallet to use those addresses as your "change" address on the other hand... For most wallets, not an easy thing... But I know Bitcoin Core allows you to specify a "custom change address" if you have "coin control" enabled:
![](https://ip.bitcointalk.org/?u=https%3A%2F%2Ftalkimg.com%2Fimages%2F2023%2F11%2F15%2Fz1e2j.png&t=665&c=hvMjhkqfoBS_tw)