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


USING: io kernel lists lists.lazy math math.primes prettyprint ;
 
: useful ( -- list )
    1 lfrom
    [ 2^ 2^ 1 lfrom [ - prime? ] with lfilter car ] lmap-lazy ;
 
10 useful ltake [ pprint bl ] leach nl