Post an anime that's NOT originally a manga.

No.6 was based off novels C:

But I think someone wrote the comic for it after the anime aired so there is one now...

going to break from my usual "dangan ronpa" answer and go with dramatical murder
i honestly have not played the game past the intro but yeah i think its pretty obvious as to why i didnt
the anime is actually really good though

Serial experiments Lain (picture)
Code Geass
Higurashi no Naku Koro ni

Madoka Magica had a manga made after the original series came out!

Gundam ZZ & Mobile Suit Gundam

Mind answering these:
Ideas for Gundam ZZ Compilation Films: link

Ideas for future dinastya Warriors Gundam titles: link