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 A231631 Least positive integer k < n with k!*(n-k) + 1 prime, or 0 if such an integer k does not exist. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Conjecture: 0 < a(n) < sqrt(n)*(log n) for all n > 2. See also the conjecture in A231516. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(4) = 2 since 1!*3 + 1 = 4 is not prime, but 2!*2 + 1 = 5 is prime. MATHEMATICA 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 *) CROSSREFS Cf. A000040, A000142, A231201, A231516, A231555, A231561, A231557 Sequence in context: A132589 A054843 A277427 * A280700 A038566 A020652 Adjacent sequences:  A231628 A231629 A231630 * A231632 A231633 A231634 KEYWORD nonn AUTHOR Zhi-Wei Sun, Nov 11 2013 STATUS approved

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Last modified September 22 05:47 EDT 2019. Contains 327287 sequences. (Running on oeis4.)