A231631 Least positive integer k < n with k!*(n-k) + 1 prime, or 0 if such an integer k does not exist.

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

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 * A377224 A280700 A356149

Adjacent sequences: A231628 A231629 A231630 * A231632 A231633 A231634

Keyword

nonn

Author

Zhi-Wei Sun, Nov 11 2013

Status

approved