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
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Aug 01 2003
EXTENSIONS
Terms a(9) and following from Jon E. Schoenfield, May 15 2010
STATUS
approved