We prove a kind of bilateral series that terminates to one side (left or right) related to Ramanujan-like series for negative powers of [Formula: see text], and conjecture a type of supercongruences associated with them. We support this conjecture by checking all the cases for many primes. In addition, we are able to prove a few of them from some terminating hypergeometric identities. Finally, we make an intriguing observation.

中文翻译：

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1/πk 的双边类拉马努金级数及其同余

对于[公式：见正文]的负幂，我们证明了一种终止于一侧（左侧或右侧）的与类拉马努金级数相关的双边级数，并推测与它们相关的一种超同余。我们通过检查许多素数的所有情况来支持这个猜想。此外，我们能够从一些终止的超几何恒等式中证明其中的一些。最后，我们做了一个有趣的观察。