user
An **ultra-useful prime** is a member of the sequence where each **a(n)** is the smallest positive integer **k** such that **2(2n) - k** is prime.

***k** must always be an odd number since 2 to any power is always even.*

Task

* Find and show here, on this page, the first **10** elements of the sequence.

Stretch

* Find and show the next several elements. (The numbers get really big really fast. Only nineteen elements have been identified as of this writing.)

See also

* OEIS:A058220 - Ultra-useful primes: smallest k such that 2^(2^n) - k is prime
assistant
The first 10 take less than a quarter second. 11 through 13, a little under 30 seconds. Drops off a cliff after that.

```
sub useful ($n) {
    (|$n).map: {
        my $p = 1 +< ( 1 +< $_ );
        ^$p .first: ($p - *).is-prime
    }
}

put useful 1..10;

put useful 11..13;

```

Output:

```
1 3 5 15 5 59 159 189 569 105
1557 2549 2439
```