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A046735
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Nontrivial (i.e., having no nontrivial factors with this property) integers which do not divide any terms of A000213.
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5
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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
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OFFSET
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1,1
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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]}];
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PROG
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(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)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition corrected by Henry Ayoola (henry.ayoola(AT)googlemail.com), Feb 03 2009
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STATUS
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approved
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