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A117706 Numbers k such that 6^k - k^6 is prime. 10
1, 7, 13, 35, 53, 115, 145, 307, 10163 (list; graph; refs; listen; history; text; internal format)
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 Miller-Rabin 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
Henri Lifchitz and Renaud Lifchitz, PRP Records.
EXAMPLE
a(2)=7 because 6^7 - 7^6 = 162287 is prime.
MATHEMATICA
Do[If[PrimeQ[(6^n-n^6)], Print[n]], {n, 1, 3000}]
PROG
(PARI) for(x=1, 1e5, ispseudoprime(p=6^x-x^6)&&print1(x", ")) \\ M. F. Hasler, Aug 20 2014
CROSSREFS
Cf. A128448.
Sequence in context: A060983 A001001 A067692 * A066673 A307762 A290947
KEYWORD
hard,more,nonn
AUTHOR
Mohammed Bouayoun (Mohammed.Bouayoun(AT)sanef.com), Apr 13 2006, Jan 08 2008
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)