A107990 Primes representing areas of cube faces where the integer part of the cube's volume is also prime.

2, 3, 5, 43, 89, 113, 131, 163, 457, 467, 509, 541, 587, 739, 773, 887, 1109, 1123, 1201, 1307, 1319, 1409, 1613, 1741, 1747, 1787, 1979, 2063, 2069, 2459, 2467, 2671, 2689, 2741, 2789, 3187, 3203, 3539, 3547, 3557, 3643, 3823, 3917, 3989, 4021, 4441, 4447

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..47.

Formula

{p in A000040: floor(p^(2/3)) in A000040}.

Example

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.

Prog

(PARI) g(n) = forprime(x=2, n, y=floor(sqrt(x)^3); if(isprime(y), print1(x, ", ")))

Crossrefs

Cf. A107989.

Sequence in context: A106820 A362957 A042469 * A117460 A281252 A208223

Adjacent sequences: A107987 A107988 A107989 * A107991 A107992 A107993

Keyword

easy,nonn

Author

Cino Hilliard, Jun 13 2005

Extensions

Offset set to 1, example expanded - R. J. Mathar, Sep 16 2009

Status

approved