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Senator Rand Paul of Kentucky often says that he campaigns where “other Republicans aren’t,” like Detroit, Alaska, and, well, on a smartphone.

The Paul campaign is releasing a smartphone app on Wednesday through the Apple and Android stores, one of the few official campaign apps of 2016 aside from one from Senator Ted Cruz of Texas. It tries to offer a blend of digital mischief and communication that has come to be a hallmark of Mr. Paul’s online campaign.

In addition to offering calendar events, campaign news and a featured video, the app lets users post their own Rand Paul memes or create an artificial selfie with the senator to share on social media. And if they know where to tap, they can find an “Easter egg” hidden game, a version of the 1978 arcade classic “Space Invaders” that features Mr. Paul’s torch logo shooting rockets at other campaigns’ logos, blasting Donald J. Trump’s “Make America Great Again” and Jeb Bush’s “Jeb!” into pixelated embers.

A common criticism of campaign apps is that they speak only to the converted; there’s no point in persuading a user who’s willing to download an app.

But there is use in reaching out to that base. Mr. Paul’s app will send push alerts when the senator is hosting an event in the area, and notify users when he is about to vote on a bill in the Senate, asking his followers how they think he should vote.

“You have a reason to download it because you can influence what happens,” said Ron Schnell, the chief technology officer of the Paul campaign and architect of the app. “It’s not just to find out about the candidate you support, it’s about letting the candidate know what you think.”

The first piece of content a user sees when beginning to scroll in the app, however, is not a game or news, but rather an option to donate.

And should a Trump or Bush logo blow up the user-controlled Paul liberty torch in the app’s hidden game, the user is chided: “You have not defeated your inferiors! Assuage your guilt by making a donation to the campaign!”