An '''ultra-useful prime''' is a member of the sequence where each <span style="font-size:125%;">'''a(n)'''</span> is the smallest positive integer <span style="font-size:125%;">'''k'''</span> such that <span style="font-size:125%;">'''2<sup>(2<sup>n</sup>)</sup> - k'''</span> 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|OEIS:A058220 - Ultra-useful primes: smallest k such that 2^(2^n) - k is prime]]
 
