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

%I A046735 #20 Mar 05 2019 08:24:43
%S A046735 2,27,91,103,163,199,203,221,247,305,371,377,397,421,551,559,757,779,
%T A046735 883,991,1021,1079,1087,1123,1189,1199,1237,1351,1521,1543,1567,1609,
%U A046735 1651,1753,1769,1799,1807,1873,1883,1919,2009,2071,2261,2539
%N A046735 Nontrivial (i.e., having no nontrivial factors with this property) integers which do not divide any terms of A000213.
%H A046735 Robert Israel, <a href="/A046735/b046735.txt">Table of n, a(n) for n = 1..1275</a>
%p A046735 nd:= proc(p) local a,b,c,r,R;
%p A046735    a:= 1; b:= 1; c:= 1; R[1,1,1]:= true;
%p A046735    do
%p A046735      r:= a+b+c mod p;
%p A046735      if r = 0 then return false fi;
%p A046735      a:= b; b:= c; c:= r;
%p A046735      if assigned(R[a,b,c]) or nops({a,b,c})=1
%p A046735          then return true
%p A046735          else R[a,b,c]:= true
%p A046735        fi;
%p A046735    od
%p A046735 end proc:
%p A046735 N:= 10^4: # to get all terms <= N
%p A046735 V:= Vector(N): Res:= NULL:
%p A046735 for n from 1 to N do
%p A046735   if V[n] = 0 then
%p A046735     if nd(n) then Res:= Res,n; V[[seq(k*n,k=2..floor(N/n))]]:= 1; fi
%p A046735   fi;
%p A046735 od:
%p A046735 Res; # _Robert Israel_, Feb 26 2017
%t A046735 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]]]];
%t A046735 okQ[n_] := Do[If[nondivisor[d], Return[n == d]], {d, Divisors[n]}];
%t A046735 Select[Range[3000], okQ] (* _Jean-François Alcover_, Mar 05 2019, from PARI *)
%o A046735 (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)))
%o A046735 is(n)=fordiv(n,d,if(nondivisor(d),return(n==d)));0 \\ _Charles R Greathouse IV_, Aug 29 2012
%K A046735 nonn
%O A046735 1,1
%A A046735 _David W. Wilson_
%E A046735 Definition corrected by Henry Ayoola (henry.ayoola(AT)googlemail.com), Feb 03 2009
%E A046735 a(1) added by _Charles R Greathouse IV_, Aug 29 2012