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Search: id:A107990
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| A107990 |
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Primes representing areas of cube faces where the integer part of the cube's volume is also prime. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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FORMULA
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{p in A000040: floor(p^(2/3)) in A000040}.
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EXAMPLE
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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.
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PROGRAM
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(PARI) g(n) = forprime(x=2, n, y=floor(sqrt(x)^3); if(isprime(y), print1(x, ", ")))
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CROSSREFS
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Sequence in context: A106713 A106820 A042469 this_sequence A117460 A136371 A060380
Adjacent sequences: A107987 A107988 A107989 this_sequence A107991 A107992 A107993
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Jun 13 2005
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EXTENSIONS
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Offset set to 1, example expanded - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 16 2009
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