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A228440
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Numbers n dividing u(n), where the Lucas sequence is defined u(i) = u(i-1) - 3*u(i-2) with initial conditions u(0)=0, u(1)=1.
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1
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1, 11, 121, 253, 1331, 2783, 5819, 11891, 14641, 29161, 30613, 64009, 130801, 133837, 161051, 273493, 320771, 336743, 558877, 640343, 670703, 704099, 895873, 1438811, 1472207, 1771561, 3008423, 3078251, 3528481, 3544453, 3704173, 6147647, 6290339, 7027801
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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 (=11), the sequence contains every nonnegative integer power of 11 (A001020 is subsequence). Other terms are formed on multiplication of 11^k by sporadic primes.
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LINKS
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EXAMPLE
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u(1)=1 and u(11)=253. Clearly n divides u(n) for these terms.
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MATHEMATICA
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nn = 10000; s = LinearRecurrence[{1, -3}, {1, 1}, nn]; t = {}; Do[
If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 06 2013 *)
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CROSSREFS
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Cf. A214733 (Lucas sequence u(n) ignoring sign).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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