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A047261
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Numbers that are congruent to {2, 4, 5} mod 6.
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9
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2, 4, 5, 8, 10, 11, 14, 16, 17, 20, 22, 23, 26, 28, 29, 32, 34, 35, 38, 40, 41, 44, 46, 47, 50, 52, 53, 56, 58, 59, 62, 64, 65, 68, 70, 71, 74, 76, 77, 80, 82, 83, 86, 88, 89, 92, 94, 95, 98, 100, 101, 104, 106, 107, 110, 112, 113, 116, 118, 119, 122, 124
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OFFSET
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1,1
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COMMENTS
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If B and C are terms in the sequence then 2*B*C is a term. B (resp. C) is a term iff B (resp. C) mod 6 = 2, 4 or 5. It follows that (2*B*C) mod 6 = (2*(B mod 6)*(C mod 6)) mod 6 = 2 or 4 and therefore 2*B*C is a term. Examples: for B=16 and C=29, 2*16*29 = 928 is a term: (2*B*C) mod 6 = (2*16*29) mod 6 = 4; (2*2*2) mod 6 = 2. - Jerzy R Borysowicz, May 24 2018
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LINKS
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FORMULA
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G.f.: x*(1+x)*(x^2+2) / ((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) = (6*n - 1 - 2*cos(2*n*Pi/3))/3.
a(3k) = 6k-1, a(3k-1) = 6k-2, a(3k-2) = 6k-4. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/6 - log(2+sqrt(3))/(2*sqrt(3)) + log(2)/3. - Amiram Eldar, Dec 16 2021
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1 + x)*(x^2 + 2)/((1 + x + x^2)*(x - 1)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Aug 16 2014 *)
Select[ Range@ 125, MemberQ[{2, 4, 5}, Mod[#, 6]] &] (* or *)
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PROG
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(Haskell)
a047261 n = a047261_list !! n
a047261_list = 2 : 4 : 5 : map (+ 6) a047261_list
(Magma) [n : n in [0..150] | n mod 6 in [2, 4, 5]]; // Wesley Ivan Hurt, Jun 14 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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EXTENSIONS
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STATUS
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approved
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