A117706 Numbers k such that 6^k - k^6 is prime.

1, 7, 13, 35, 53, 115, 145, 307, 10163

Offset: 1

Author

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

Keywords

• hard
• more
• nonn

Comments

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

Examples

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

Links

• Henri Lifchitz and Renaud Lifchitz, PRP Records.

Crossrefs

Cf. A128448.

Programs

Mathematica

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

PARI

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

Extensions

a(9) found by Donovan Johnson.