A125163 - OEIS

%I #22 Dec 16 2024 19:15:51

%S 8,14,20,24,26,32,33,34,38,44,48,50,54,56,62,63,64,68,74,75,76,80,84,

%T 86,90,92,93,94,98,104,110,114,116,117,118,120,122,123,124,128,132,

%U 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

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

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

%e 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,...}.

%e Thus a(1) = 8, a(2) = 14, a(3) = 20, a(4) = 24, a(5) = 26, a(6)-a(8) = {32,33,34}.

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

%o (PARI) b(n)=c=0;for(k=1,n,if(ispseudoprime(k!+n),c++));c

%o n=1;while(n<500,if(!b(n),print1(n,", "));n++) \\ _Derek Orr_, Oct 15 2014

%Y 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).

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 21 2006

%E More terms from _Derek Orr_, Oct 15 2014

%E Edited by _Michel Marcus_, Jul 29 2018