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A047249
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Numbers that are congruent to {3, 4, 5} mod 6.
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1
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3, 4, 5, 9, 10, 11, 15, 16, 17, 21, 22, 23, 27, 28, 29, 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 71, 75, 76, 77, 81, 82, 83, 87, 88, 89, 93, 94, 95, 99, 100, 101, 105, 106, 107, 111, 112, 113, 117, 118, 119, 123, 124
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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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G.f.: x*(3+x+x^2+x^3) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 2*n-cos(2*n*Pi/3)+sin(2*n*Pi/3)/sqrt(3).
a(3k) = 6k-1, a(3k-1) = 6k-2, a(3k-2) = 6k-3. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (9-2*sqrt(3))*Pi/36 + log(2)/6 - log(2+sqrt(3))/(2*sqrt(3)). - Amiram Eldar, Dec 16 2021
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MAPLE
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MATHEMATICA
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Select[Range[150], MemberQ[{3, 4, 5}, Mod[#, 6]]&] (* Harvey P. Dale, Nov 21 2012 *)
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PROG
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(Magma) [n : n in [0..150] | n mod 6 in [3..5]]; // Wesley Ivan Hurt, Jun 10 2016
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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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