Only two balancing numbers $$B_1=1$$ and $$B_3=35$$ are one away from a perfect powers. Furthermore, each balancing-like sequence has at most three terms which are one away from perfect squares.

中文翻译：

---

平衡和类似平衡的数字远离完美的幂

只有两个平衡数 $$B_1=1$$ 和 $$B_3=35$$ 与完美幂相差一个。此外，每个类平衡序列至多具有三个与完美平方相差一个的项。