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 A086758 a(n) is the smallest m such that the integer part of the first n powers of m^(1/n) are primes. 1
 2, 5, 13, 31, 631, 173, 409, 967, 3450844193, 39661481813, 2076849234433, 52134281654579, 14838980942616539, 260230524377962793, 4563650703502319197, 80032531899785490253, 172111744128569095516889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. REFERENCES R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 1.75, p. 69. LINKS Martin Raab, Table of n, a(n) for n = 1..53 Carlos Rivera, Puzzle 227. Research Problem 1.75, Prime Puzzles and Problems Connection. FORMULA For[m=1, Union[Table[PrimeQ[Floor[Prime[m]^(k/n)]], {k, n}]]!={True}, m++ ]; Prime[m] EXAMPLE 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. MATHEMATICA Do[Print[For[m=1, Union[Table[PrimeQ[Floor[Prime[m]^(k/n)]], {k, n}]]!={True}, m++ ]; Prime[m]], {n, 8}] CROSSREFS Sequence in context: A056367 A082733 A095134 * A179257 A116702 A098156 Adjacent sequences:  A086755 A086756 A086757 * A086759 A086760 A086761 KEYWORD nonn AUTHOR Farideh Firoozbakht, Aug 01 2003 EXTENSIONS Terms a(9) and following from Jon E. Schoenfield, May 15 2010 STATUS approved

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Last modified August 11 02:42 EDT 2020. Contains 336418 sequences. (Running on oeis4.)