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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A273844 A294678 A206585 * A038625 A280089 A041801

Adjacent sequences: A046732 A046733 A046734 * A046736 A046737 A046738

Keyword

nonn

Author

David W. Wilson

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

Status

approved