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A016051
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Numbers of the form 9*k+3 or 9*k+6.
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5
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3, 6, 12, 15, 21, 24, 30, 33, 39, 42, 48, 51, 57, 60, 66, 69, 75, 78, 84, 87, 93, 96, 102, 105, 111, 114, 120, 123, 129, 132, 138, 141, 147, 150, 156, 159, 165, 168, 174, 177, 183, 186, 192, 195, 201, 204, 210, 213, 219, 222, 228, 231, 237, 240
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n+1) = a(n) + its digital root in decimal base.
a(n) = a(n-1) + a(n-2) - a(n-3) = 9*n/2 - 9/4 - 3*(-1)^n/4.
G.f: 3*x*(1+x+x^2)/((1+x)*(x-1)^2). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(9*sqrt(3)). - Amiram Eldar, Sep 26 2022
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MATHEMATICA
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LinearRecurrence[{1, 1, -1}, {3, 6, 12}, 60] (* or *) #+{3, 6}&/@(9*Range[0, 30])//Flatten (* Harvey P. Dale, Oct 04 2021 *)
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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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STATUS
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approved
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