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A083105
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Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2).
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4
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62638280004239857, 49463435743205655, 112101715747445512, 161565151490651167, 273666867238096679, 435232018728747846, 708898885966844525, 1144130904695592371, 1853029790662436896
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OFFSET
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0,1
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COMMENTS
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a(0) = 62638280004239857, a(1) = 49463435743205655. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by D. E. Knuth in 1990.
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REFERENCES
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R. L. Graham, Math. Mag. 37, 1964, pp. 322-324.
D. E. Knuth, Math. Mag. 63, 1990, pp. 21-25.
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LINKS
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Table of n, a(n) for n=0..8.
Tanya Khovanova, Recursive Sequences
J. W. Nicol, A Fibonacci-like sequence of composite numbers
Prime Puzzles, Problem 31. Fibonacci- all composites sequence
Index to sequences with linear recurrences with constant coefficients, signature (1,1).
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FORMULA
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G.f.: (62638280004239857-13174844261034202*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]
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CROSSREFS
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Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083216, A082411.
Sequence in context: A204189 A051167 A155057 * A115499 A104837 A008923
Adjacent sequences: A083102 A083103 A083104 * A083106 A083107 A083108
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KEYWORD
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nonn,easy
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AUTHOR
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Harry J. Smith, Apr 23 2003
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STATUS
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approved
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