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A228439
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Numbers n dividing u(n), where the Lucas sequence is defined u(i) = u(i-1) - 2*u(i-2) with initial conditions u(0)=0, u(1)=1.
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0
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1, 7, 49, 343, 2401, 4753, 16807, 33271, 76783, 117649, 232897, 461041, 537481, 823543, 1630279, 3227287, 3762367, 5764801
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OFFSET
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1,2
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COMMENTS
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Since the absolute value of the discriminant of the characteristic polynomial is prime (=7), the sequence contains every nonnegative integer power of 7. Other terms are formed on multiplication of 7^k by sporadic primes.
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LINKS
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EXAMPLE
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For n=0,1,...10, there is u(n)=0,1,1,-1,-3,-1,5,7,-3,-17,-11. Clearly only n=1 and n=7 satisfy n divides u(n).
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MATHEMATICA
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nn = 10000; s = LinearRecurrence[{1, -2}, {1, 1}, nn]; t = {}; Do[If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 08 2013 *)
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CROSSREFS
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Cf. A107920 (Lucas Sequence u(n)=u(n-1)-2u(n-2)).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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