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Numbers k such that 12*13^k - 1 is prime.
1

%I #50 Nov 12 2024 14:31:45

%S 0,2,7,11,36,164,216,302,311,455,738,1107,2244,3326,4878,8067,46466

%N Numbers k such that 12*13^k - 1 is prime.

%C Williams primes to base 12.

%H Steven Harvey, <a href="http://harvey563.tripod.com/wills.txt">Williams primes</a>

%H H. C. Williams, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf">The primality of certain integers of the form 2Ar^n - 1</a>, Acta Arith. 39 (1981), 7-17.

%t Select[Range[0, 10000], PrimeQ[12*13^n-1] &]

%o (PARI) for(n=0, 10000, if(isprime(12*13^n-1), print1(n, ", ")))

%o (Magma) [n: n in [0..10000] |IsPrime(12*13^n-1)];

%Y Cf. A003307, A272057, A046865, A079906, A046866, A268061, A268356, A056725, A046867, A079907, A273523.

%K nonn,more,hard,changed

%O 1,2

%A _Tim Johannes Ohrtmann_, Feb 15 2018

%E a(16) from _Michael S. Branicky_, Sep 14 2022

%E a(17) from _Michael S. Branicky_, Nov 12 2024