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A086758
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a(n) is the smallest m such that the integer part of the first n powers of m^(1/n) are primes.
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1
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2, 5, 13, 31, 631, 173, 409, 967, 3450844193, 39661481813, 2076849234433, 52134281654579, 14838980942616539, 260230524377962793, 4563650703502319197, 80032531899785490253, 172111744128569095516889
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OFFSET
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1,1
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COMMENTS
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All terms of this sequence must be primes because floor((a(n)^(1/n))^n) = a(n).
Floor[(a(8)^(1/8))^k] = floor[(1287/545)^k] for k=1..10 (see puzzle 227). If a(9) exists it must be greater than 22000000.
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 1.75, p. 69.
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LINKS
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FORMULA
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For[m=1, Union[Table[PrimeQ[Floor[Prime[m]^(k/n)]], {k, n}]]!={True}, m++ ]; Prime[m]
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EXAMPLE
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a(5)=631 because floor(631^(1/5)) = 3, floor(631^(2/5)) = 13, floor(631^(3/5)) = 47, floor[631^(4/5)) = 173 and floor(631^(5/5)) = 631 are primes and 631 is the smallest m with this property.
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MATHEMATICA
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Do[Print[For[m=1, Union[Table[PrimeQ[Floor[Prime[m]^(k/n)]], {k, n}]]!={True}, m++ ]; Prime[m]], {n, 8}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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