

A117706


Numbers k such that 6^k  k^6 is prime.


10




OFFSET

1,2


COMMENTS

a(9) found by Donovan Johnson.
Comment from Donovan Johnson: A117705 and A117706 are both Fermat probable prime to four bases. They have also passed a MillerRabin primality test in five randomly chosen bases. I checked the n values up to 70000 for A117705 and n values up to 60000 for A117706. No additional primes or probable primes were found.
The actual primes are listed in A243114.  M. F. Hasler, Aug 20 2014
From the Lifchitz link: 100193 and 114433 are also in this sequence.  Robert Price, Mar 27 2019


LINKS

Table of n, a(n) for n=1..9.
Henri Lifchitz and Renaud Lifchitz, PRP Records.


EXAMPLE

a(2)=7 because 6^7  7^6 = 162287 is prime.


MATHEMATICA

Do[If[PrimeQ[(6^nn^6)], Print[n]], {n, 1, 3000}]


PROG

(PARI) for(x=1, 1e5, ispseudoprime(p=6^xx^6)&&print1(x", ")) \\ M. F. Hasler, Aug 20 2014


CROSSREFS

Cf. A128448.
Sequence in context: A060983 A001001 A067692 * A066673 A307762 A290947
Adjacent sequences: A117703 A117704 A117705 * A117707 A117708 A117709


KEYWORD

hard,more,nonn


AUTHOR

Mohammed Bouayoun (Mohammed.Bouayoun(AT)sanef.com), Apr 13 2006, Jan 08 2008


STATUS

approved



