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%I #23 Jan 01 2023 09:44:11
%S 2,6,7,93,15,372,421,759,7426,9087
%N Least k such that k^(3^n)*(k^(3^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 sequence is a subset of A205506 with only m=3^n, which is similar to A153438.
%C Search limits: a(10) > 35000, a(11) > 3500.
%F a(n) = A085398(2*3^(n+1)). - _Jinyuan Wang_, Jan 01 2023
%e When k = 7, k^18 - k^9 + 1 is prime. Since this isn't prime for k < 7, a(2) = 7.
%t a246120[n_Integer] := Module[{k = 1},
%t While[! PrimeQ[k^(3^n)*(k^(3^n) - 1) + 1], k++]; k]; a246120 /@ Range[0, 9] (* _Michael De Vlieger_, Aug 15 2014 *)
%o (PARI)
%o a(n)=k=1;while(!ispseudoprime(k^(3^n)*(k^(3^n)-1)+1),k++);k
%o n=0;while(n<100,print1(a(n),", ");n++) \\ _Derek Orr_, Aug 14 2014
%Y Cf. A056993, A085398, A101406, A153436, A153438, A205506, A246119, A246121.
%K nonn,more,hard
%O 0,1
%A _Serge Batalov_, Aug 14 2014
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