This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117706 #21 Nov 20 2024 16:29:24
%S A117706 1,7,13,35,53,115,145,307,10163
%N A117706 Numbers k such that 6^k - k^6 is prime.
%C A117706 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.
%C A117706 The actual primes are listed in A243114. - _M. F. Hasler_, Aug 20 2014
%C A117706 From the Lifchitz link: 100193 and 114433 are also in this sequence. - _Robert Price_, Mar 27 2019
%H A117706 Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=6%5En-n%5E6&action=Search">PRP Records</a>.
%e A117706 a(2)=7 because 6^7 - 7^6 = 162287 is prime.
%t A117706 Do[If[PrimeQ[(6^n-n^6)],Print[n]],{n,1,3000}]
%o A117706 (PARI) for(x=1,1e5,ispseudoprime(p=6^x-x^6)&&print1(x", ")) \\ _M. F. Hasler_, Aug 20 2014
%Y A117706 Cf. A128448.
%K A117706 hard,more,nonn
%O A117706 1,2
%A A117706 Mohammed Bouayoun (Mohammed.Bouayoun(AT)sanef.com), Apr 13 2006, Jan 08 2008
%E A117706 a(9) found by _Donovan Johnson_.