A046735 Nontrivial (i.e., having no nontrivial factors with this property) integers which do not divide any terms of A000213.

2, 27, 91, 103, 163, 199, 203, 221, 247, 305, 371, 377, 397, 421, 551, 559, 757, 779, 883, 991, 1021, 1079, 1087, 1123, 1189, 1199, 1237, 1351, 1521, 1543, 1567, 1609, 1651, 1753, 1769, 1799, 1807, 1873, 1883, 1919, 2009, 2071, 2261, 2539

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..1275

Programs

Maple

nd:= proc(p) local a,b,c,r,R;
   a:= 1; b:= 1; c:= 1; R[1,1,1]:= true;
   do
     r:= a+b+c mod p;
     if r = 0 then return false fi;
     a:= b; b:= c; c:= r;
     if assigned(R[a,b,c]) or nops({a,b,c})=1
         then return true
         else R[a,b,c]:= true
       fi;
   od
end proc:
N:= 10^4: # to get all terms <= N
V:= Vector(N): Res:= NULL:
for n from 1 to N do
  if V[n] = 0 then
    if nd(n) then Res:= Res,n; V[[seq(k*n,k=2..floor(N/n))]]:= 1; fi
  fi;
od:
Res; # Robert Israel, Feb 26 2017

Mathematica

nondivisor[n_] := Module[{a = 1, b = 1, c = 1, t}, For[i = 1, i <= n^2, i++, t = Mod[a+b+c, n]; If[t != 0, a = b; b = c; c = t, Return[False]]; If[c == 1 && b == 1 && a == 1, Return[True]]]];
okQ[n_] := Do[If[nondivisor[d], Return[n == d]], {d, Divisors[n]}];
Select[Range[3000], okQ] (* Jean-François Alcover, Mar 05 2019, from PARI *)

PARI

nondivisor(n)=my(a=1,b=1,c=1,t);for(i=1,n^2,t=(a+b+c)%n;if(t,a=b;b=c;c=t,return(0));if(c==1&&b==1&&a==1,return(1)))
is(n)=fordiv(n,d,if(nondivisor(d),return(n==d)));0 \\ Charles R Greathouse IV, Aug 29 2012

Extensions

Definition corrected by Henry Ayoola (henry.ayoola(AT)googlemail.com), Feb 03 2009

a(1) added by Charles R Greathouse IV, Aug 29 2012