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A246120
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Least k such that k^(3^n)*(k^(3^n) - 1) + 1 is prime.
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4
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OFFSET
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0,1
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COMMENTS
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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.
Search limits: a(10) > 35000, a(11) > 3500.
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LINKS
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FORMULA
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EXAMPLE
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When k = 7, k^18 - k^9 + 1 is prime. Since this isn't prime for k < 7, a(2) = 7.
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MATHEMATICA
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a246120[n_Integer] := Module[{k = 1},
While[! PrimeQ[k^(3^n)*(k^(3^n) - 1) + 1], k++]; k]; a246120 /@ Range[0, 9] (* Michael De Vlieger, Aug 15 2014 *)
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PROG
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(PARI)
a(n)=k=1; while(!ispseudoprime(k^(3^n)*(k^(3^n)-1)+1), k++); k
n=0; while(n<100, print1(a(n), ", "); n++) \\ Derek Orr, Aug 14 2014
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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