0%

Problem 119


Problem 119


Digit power sum

The number 512 is interesting because it is equal to the sum of its digits raised to some power: 5 + 1 + 2 = 8, and 83 = 512. Another example of a number with this property is 614656 = 284.

We shall define an to be the nth term of this sequence and insist that a number must contain at least two digits to have a sum.

You are given that a2 = 512 and a10 = 614656.

Find a30.


数字和的幂

512是一个有趣的数,因为它等于其各位数字和的幂:5 + 1 + 2 = 8,而83 = 512。拥有同样性质的数的另一个例子是614656 = 284

记an是这类数中的第n个,并且约定一个数至少需要两位数字才有各位数字和。

已知a2 = 512以及a10 = 614656。

求a30