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

Author

Zhi-Wei Sun, Nov 11 2013

Keywords

• nonn

Comments

Conjecture: 0 < a(n) < sqrt(n)*(log n) for all n > 2.

See also the conjecture in A231516.

Examples

			a(4) = 2 since 1!*3 + 1 = 4 is not prime, but 2!*2 + 1 = 5 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000142, A231201, A231516, A231555, A231561, A231557

Programs

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 *)