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A047587
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Numbers that are congruent to {0, 2, 3, 5, 6, 7} mod 8.
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3
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0, 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 42, 43, 45, 46, 47, 48, 50, 51, 53, 54, 55, 56, 58, 59, 61, 62, 63, 64, 66, 67, 69, 70, 71, 72, 74, 75, 77, 78, 79, 80, 82, 83, 85, 86, 87
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x^2*(2+x+2*x^2+x^3+x^4+x^5)/((x-1)^2*(1+x+x^2+x^3+x^4+x^5)).
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
a(n) = (24*n-15+3*cos(n*Pi)-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/18.
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = (8-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - 3*(sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 27 2021
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MAPLE
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MATHEMATICA
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Select[Range[0, 150], MemberQ[{0, 2, 3, 5, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Oct 04 2011 *)
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PROG
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(Magma) [n : n in [0..100] | n mod 8 in [0, 2, 3, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 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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