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A231735
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Least positive k such that n*k^k - 1 is a prime, or 0 if no such k exists.
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3
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2, 2, 1, 1, 2, 1, 1128, 1, 0, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 14, 1, 0, 2, 2, 6, 206, 1, 1590, 1, 2, 11, 2, 3
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OFFSET
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1,1
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COMMENTS
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For all odd numbers n > 3, a(n) is even.
For all odd numbers n > 1, a(n^2) = 0. (End)
Other known terms: a(38) = 1, a(39) = 6, a(40) = 6, a(41) = 2, a(42) = 1, a(44) = 8, a(45) = 22, a(47) = 48, a(48) = 7, a(49) = 0, a(50) = 14.
Other unknown terms: a(43) > 5000, a(46) > 1000, a(51) > 1000. (End)
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LINKS
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FORMULA
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EXAMPLE
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The least k > 0 such that 5*k^k - 1 is a prime is k = 2, so a(5) = 2.
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MATHEMATICA
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Table[If[And[n > 1, OddQ@ Sqrt@ n], 0, If[And[n > 3, OddQ@ n], Block[{k = 2}, While[! PrimeQ[n*k^k - 1], k += 2]; k], Block[{k = 1}, While[! PrimeQ[n*k^k - 1], k++]; k]]], {n, 36}] (* Michael De Vlieger, Sep 29 2019 *)
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PROG
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(PARI) a(n) = if(sqrt(n)%2==1 && n>1, 0, for(k=1, oo, if(ispseudoprime(n*k^k-1), return(k)))); \\ Jinyuan Wang, Mar 05 2020
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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