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A246121 Least k such that k^(6^n)*(k^(6^n)-1)+1 is prime. 3

%I

%S 2,3,88,28,688,7003,1925

%N Least k such that k^(6^n)*(k^(6^n)-1)+1 is prime.

%C Numbers of the form k^m*(k^m-1)+1 with m > 0, k > 1 may be primes only if m is 3-smooth, because these numbers are Phi(6,k^m) and cyclotomic factorizations apply to any prime divisors >3. This series is a subset of A205506 with only m=6^n.

%C Numbers of this form are Generalized unique primes. a(6) generates a 306477-digit prime.

%H C.Caldwell, <a href="http://primes.utm.edu/top20/page.php?id=44">Generalized unique primes</a>

%e When k = 88, k^72-k^36+1 is prime. Since this isn't prime for k < 88, a(2) = 88.

%o (PARI) a(n)=k=1; while(!ispseudoprime(k^(6^n)*(k^(6^n)-1)+1), k++); k

%o n=0; while(n<100, print1(a(n), ", "); n++)

%Y Cf. A205506, A246119, A246120, A153438, A101406, A153436, A056993.

%K nonn,more,hard

%O 0,1

%A _Serge Batalov_, Aug 14 2014

%E a(6) from _Serge Batalov_, Aug 15 2014

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Last modified February 26 14:18 EST 2021. Contains 341632 sequences. (Running on oeis4.)