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A231631
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Least positive integer k < n with k!*(n-k) + 1 prime, or 0 if such an integer k does not exist.
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7
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0, 1, 1, 2, 1, 3, 1, 2, 3, 2, 1, 4, 1, 3, 3, 2, 1, 4, 1, 2, 3, 2, 1, 3, 2, 3, 6, 2, 1, 3, 1, 2, 3, 6, 2, 3, 1, 2, 6, 3, 1, 5, 1, 6, 5, 2, 1, 3, 3, 2, 4, 2, 1, 3, 2, 2, 6, 2, 1, 11, 1, 5, 5, 3, 2, 3, 1, 5, 3, 2, 1, 6, 1, 7, 3, 2, 2, 4, 1, 2, 6, 4, 1, 3, 2, 3, 4, 2, 1, 3, 2, 2, 3, 3, 6, 7, 1, 2, 3, 2
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OFFSET
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1,4
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COMMENTS
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Conjecture: 0 < a(n) < sqrt(n)*(log n) for all n > 2.
See also the conjecture in A231516.
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LINKS
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EXAMPLE
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a(4) = 2 since 1!*3 + 1 = 4 is not prime, but 2!*2 + 1 = 5 is prime.
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MATHEMATICA
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Do[Do[If[PrimeQ[x!*(n-x)+1], Print[n, " ", x]; Goto[aa]], {x, 1, n-1}];
Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 100}]
lpik[n_]:=Module[{k=1}, While[!PrimeQ[k!(n-k)+1], k++]; k]; Join[{0}, Array[ lpik, 100, 2]] (* Harvey P. Dale, Apr 19 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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