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A079253
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a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is even".
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10
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0, 3, 5, 6, 7, 8, 10, 12, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 96
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OFFSET
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0,2
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REFERENCES
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Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585
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LINKS
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FORMULA
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For a formula for a(n) see A079000.
a(a(n)) = 2n+4 for n >= 1.
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EXAMPLE
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a(1) cannot be 1 because that would imply that the first term is even; it cannot be 2 because then the first term would be even despite 1's not being in the sequence; therefore a(1)=3, which creates no contradictions and the third term is the first even term of the sequence.
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MATHEMATICA
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a[0] = 0; a[n_] := With[{k = 2^Floor[Log[2, (n+4)/6]]}, (Abs[n - 9k + 4] - 3k + 3n + 6)/2 - 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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STATUS
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approved
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