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A246121
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Least k such that k^(6^n)*(k^(6^n) - 1) + 1 is prime.
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3
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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=6^n.
Numbers of this form are Generalized unique primes. a(6) generates a 306477-digit prime.
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LINKS
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FORMULA
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EXAMPLE
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When k = 88, k^72 - k^36 + 1 is prime. Since this isn't prime for k < 88, a(2) = 88.
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PROG
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(PARI) a(n)=k=1; while(!ispseudoprime(k^(6^n)*(k^(6^n)-1)+1), k++); k
n=0; while(n<100, print1(a(n), ", "); n++)
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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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EXTENSIONS
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STATUS
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approved
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