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A047212
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Numbers that are congruent to {0, 2, 4} mod 5.
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28
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0, 2, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 25, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 65, 67, 69, 70, 72, 74, 75, 77, 79, 80, 82, 84, 85, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 104, 105, 107
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OFFSET
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1,2
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COMMENTS
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Also numbers k such that k*(k+1)*(k+3) is divisible by 5. - Bruno Berselli, Dec 28 2017
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
G.f.: x^2*(2 + 2*x + x^2)/((1 - x)^2*(1 + x + x^2)). - Bruno Berselli, Mar 31 2011
a(n) = (15*n - 12 + 3*cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/9.
a(3*k) = 5*k-1, a(3*k-1) = 5*k-3, a(3*k-2) = 5*k-5. (End)
Sum_{n>=2} (-1)^n/a(n) = log(2)/5 + arccosh(7/2)/(2*sqrt(5)) - sqrt(1-2*sqrt(5)/5)*Pi/5. - Amiram Eldar, Dec 10 2021
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [n : n in [0..140] | n mod 5 in [0, 2, 4]]; // Vincenzo Librandi, Mar 31 2011
(Magma) &cat[[n, n+2, n+4]: n in [0..90 by 5]]; // Bruno Berselli, Mar 31 2011
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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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