2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2^1000 ?

Permalink: http://projecteuler.net/problem=16

Are you kidding me?

- Find 1000th
*power of two* - Sum its digits

In Clojure Euler: Problem 008 we learned how to sum digits in the number. Just gentle reminder:

```
(defn sum-of-digits [n]
(reduce + (map #(- (int %) 48) (seq (str n)))))
```

Now, let's create sequence of powers of two:

```
(defn powers-of-2 []
(iterate (partial * 2) 1))
```

Unfortunately, this sequence throws `integer overflow`

on the `64th`

element.
We can fix that using *long arithmetics*, which known as `BigInteger`

in Java.
Change `1`

to `1N`

.

```
(iterate (partial * 2) 1N)
```

Another way is to use **automatic promotion** operator (`+'`

, `*'`

).
If result of some operation is not suitable for some type,
instead of invalid computation and runtime exception, clojure automatically promotes
the type to suitable one (*for example* `Long.MAX_VALUE +' 1`

*works fine and produces
correct result with type of* `BigInteger`

):

```
(iterate (partial *' 2) 1)
```

Choose `powers-of-2`

that you prefer and final result will look like this:

```
(sum-of-digits (last (take 1001 (powers-of-2))))
```

**P.S.** Automatic promotion is a beatiful thing. But be aware about losing in
speed of calculations. Also, no way back. If promotion happened, *depromotion* won't.