%I #10 Dec 04 2018 20:45:25
%S 2,3,5,43,89,113,131,163,457,467,509,541,587,739,773,887,1109,1123,
%T 1201,1307,1319,1409,1613,1741,1747,1787,1979,2063,2069,2459,2467,
%U 2671,2689,2741,2789,3187,3203,3539,3547,3557,3643,3823,3917,3989,4021,4441,4447
%N Primes representing areas of cube faces where the integer part of the cube's volume is also prime.
%C If the area of a single face of the cube is p, the volume is V=(sqrt(p))^3, and we look for cases where floor(V) and p are both prime.
%F {p in A000040: floor(p^(2/3)) in A000040}.
%e If the area of the cube is the prime p = 5, the side length is sqrt(5), the volume is 5^(3/2) = 11.18033..., and the truncated (floor) value of the volume is 11, a prime, which puts the prime p=5 to the sequence.
%o (PARI) g(n) = forprime(x=2,n,y=floor(sqrt(x)^3);if(isprime(y),print1(x, ",")))
%Y Cf. A107989.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Jun 13 2005
%E Offset set to 1, example expanded - _R. J. Mathar_, Sep 16 2009