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%I #22 Jul 04 2021 07:52:21
%S 2,3,7,29,41,67,1327,1399,2027,69371,86689,355039
%N Numbers k such that 7^k - 6^k is prime.
%C Terms greater than 1000 often correspond only to strong probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=7%5Ep-6%5Ep">Top probable primes of the form 7^p-6^p</a>
%e 7^2 - 6^2 = 49 - 36 = 13, which is prime, so 2 is in the sequence.
%e 7^3 - 6^3 = 343 - 216 = 127, which is prime, so 3 is in the sequence.
%t Select[Range[100], PrimeQ[7^# - 6^#] &] (* _Alonso del Arte_, Sep 04 2013 *)
%o (PARI) is(n)=ispseudoprime(7^n-6^n) \\ _Charles R Greathouse IV_, Feb 20 2017
%Y Cf. A000043, A057468, A059801, A059802, A062572-A062666.
%K nonn,hard
%O 1,1
%A _Mike Oakes_, May 18 2001, May 19 2001
%E Two more terms (69371 and 86689) found by Predrag Minovic in 2004 corresponding to probable primes with 58626 and 73261 digits. - _Jean-Louis Charton_, Oct 06 2010
%E New term 355039 found by _Jean-Louis Charton_ in May 2011 corresponding to a probable prime with 300043 digits.