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A076921
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Smallest number such that the highest common factor of pair of successive terms follows the pattern 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, ..., i.e., b(2n-1) = b(2n) = n given by A004526.
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1
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1, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 121, 132, 144, 156, 169, 182, 196, 210, 225, 240, 256, 272, 289, 306, 324, 342, 361, 380, 400, 420, 441, 462, 484, 506, 529, 552, 576, 600, 625, 650, 676, 702, 729, 756, 784
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OFFSET
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1,3
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COMMENTS
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(1) a(2n) = n^2, a(2n-1) = n(n+1) = twice the n-th triangular number. (2) Geometric mean of the successive squares interleaved between them.
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LINKS
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FORMULA
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Empirical: a(n+1) + a(n) = binomial(n+1,2), a(1) = a(2) = 1. - G. C. Greubel, Oct 29 2017
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MATHEMATICA
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Join[{1}, LinearRecurrence[{2, 0, -2, 1}, {1, 2, 4, 6}, 50]] (* G. C. Greubel, Oct 29 2017 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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