In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book Recreations in the Theory of Numbers.
![R_n^{(b)}={b^n-1\over b-1}\qquad\,\!](/Images/godic/202502/07/4e47093bc66782c8d81788b34cf4152d2653.png")
![R_0=0\,\!](/Images/godic/202502/07/2f674b9593dc0edf3bf6c0cee9c570822653.png")
![R_n=bR_{n-1}+1\,\!](/Images/godic/202502/07/13b744f62abfe336989db2e973651c8b2653.png")
![b\,\!](/Images/godic/202502/07/6f1f9c73279ad1872b1fa74df9858c5c2653.png")
是进位制的底。在这篇文章，循环单位都是指十进制中的。