A125163 Numbers m such that no prime exists of the form k! + m; or A125162(m) = 0.

8, 14, 20, 24, 26, 32, 33, 34, 38, 44, 48, 50, 54, 56, 62, 63, 64, 68, 74, 75, 76, 80, 84, 86, 90, 92, 93, 94, 98, 104, 110, 114, 116, 117, 118, 120, 122, 123, 124, 128, 132, 134, 140, 141, 142, 144, 146, 152, 153, 154, 158, 159, 160, 164, 168, 170, 174, 176, 182, 183, 184, 186, 188, 194, 200, 201, 202, 204, 206, 207, 208, 212

Offset: 1

Author

Alexander Adamchuk, Nov 21 2006

Keywords

• nonn

Comments

Terms are the indices of zeros in A125162, i.e. A125162[a(n)] = 0.

Examples

			A125162 begins {1,1,1,1,3,1,4,0,1,1,5,1,3,0,1,1,6,1,7,0,1,1,6,0,1,0,1,1,6,1,9,0,0,0,3,1,11,0,1,1,9,1,5,0,1,1,10,0,2,0,1,1,9,0,2,0,1,1,10,1,9,0,0,0,3,1,9,0,1,1,8,1,9,0,0,0,5,1,9,0,1,1,11,0,1,0,1,1,8,0,3,0,0,0,2,1,10,0,1,1,...}.
Thus a(1) = 8, a(2) = 14, a(3) = 20, a(4) = 24, a(5) = 26, a(6)-a(8) = {32,33,34}.
		

Crossrefs

Cf. A125162 = number of primes of the form k! + n. Cf. A125164 = numbers n such that no prime exists of the form (k! + 3n - 1), (k! + 3n), (k! + 3n + 1).

Programs

Mathematica

k={};Do[If[Length[Select[Range[m],PrimeQ[#!+m]&]]==0,AppendTo[k,m]],{m,212}];k (* James C. McMahon, Dec 16 2024 *)

PARI

b(n)=c=0;for(k=1,n,if(ispseudoprime(k!+n),c++));c
n=1;while(n<500,if(!b(n),print1(n,", "));n++) \\ Derek Orr, Oct 15 2014

Extensions

More terms from Derek Orr, Oct 15 2014

Edited by Michel Marcus, Jul 29 2018