 If you liked
Nejimaki Seirei Senki: Tenkyou no Alderamin
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 ...then you might like
Tensai Ouji no Akaji Kokka Saisei Jutsu
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Alderamin is a far superior attempt at the show that "Genius Prince" tries to be.
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Recommended by IAmSovereign
Tensai is the only anime I've found that comes even close to capturing a similar essence to Alderamin on the Sky. The plots are not exactly similar, but the tone of the comedy and the underlying competence of the characters, the depth of the characters' relationships with each other, and the chaotic unknown of where their adventures will take them next...so refreshing. Another piece of media with a similar feel is the webcomic Girl Genius.
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Recommended by Sporcupine
Both shows are non iseaki war strategy anime with similar setting. Also, the protagonists are lazy geniuses with some sidekick/partner in a similar position. Alderamin on the Sky is a bit more serious and have a more interesting production. But The Genius Prince's Guide to Raising a Nation Out of Debt shows a lot of promise.
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Recommended by theboynamedcrow