%I
%S 1,4,8,16,32,81,144,225,343,576
%N Perfect powers that are the difference of two nonnegative Fibonacci numbers.
%C Listed 10 terms are 1, 2^2, 2^3, 2^4, 2^5, 3^4, 12^2, 15^2, 3^5, 24^2.
%C 1, 4, 8, 16, 32, 81, 343 are also members of A000961.
%C 1, 4, 8, 16, 144 are in the intersection of this sequence and A272575.
%C Is this sequence finite?
%C If a(11) exists, it must be larger than 10^2000.  _Giovanni Resta_, May 25 2016
%e 32 is a term because 32 = 2^5 = 34  2 = Fibonacci(9)  Fibonacci(3).
%p isA272712 := proc(n)
%p isA001597(n) and isA007298(n) ; #uses code in A001597 and A007298
%p end proc:
%p for n from 1 do
%p if isA272712(n) then
%p printf("%d\n",n) ;
%p end if;
%p end do: # _R. J. Mathar_, May 25 2016
%Y Cf. A007298, A001597, A219114, A272575.
%K nonn,more
%O 1,2
%A _Altug Alkan_, May 05 2016
