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A106612
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a(n) = numerator(n/(n+11)).
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25
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 4, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 5, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 6, 67, 68, 69, 70, 71, 72, 73, 74, 75
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OFFSET
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0,3
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COMMENTS
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In general, the numerators of n/(n+p) for prime p and n >= 0, form a sequence with the g.f.: x/(1-x)^2 - (p-1)*x^p/(1-x^p)^2. - Paul D. Hanna, Jul 27 2005
a(n) <> n iff n = 11 * k, in this case, a(n) = k. - Bernard Schott, Feb 19 2019
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,-1).
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FORMULA
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G.f.: x/(1-x)^2 - 10*x^11/(1-x^11)^2. - Paul D. Hanna, Jul 27 2005
a(n) = lcm(n,11)/11.
Dirichlet g.f.: zeta(s-1)*(1-10/11^s). (End)
Multiplicative with a(11^e) = 11^(e-1), and a(p^e) = p^e if p != 11.
Sum_{k=1..n} a(k) ~ (111/242) * n^2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 21*log(2)/11. - Amiram Eldar, Sep 08 2023
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MAPLE
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21}, 80] (* Harvey P. Dale, Jul 05 2021 *)
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PROG
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(Sage) [lcm(n, 11)/11 for n in range(0, 54)] # Zerinvary Lajos, Jun 09 2009
(PARI) vector(100, n, n--; numerator(n/(n+11))) \\ G. C. Greubel, Feb 19 2019
(GAP) List([0..80], n->NumeratorRat(n/(n+11))); # Muniru A Asiru, Feb 19 2019
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CROSSREFS
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KEYWORD
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nonn,frac,mult,easy
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AUTHOR
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STATUS
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approved
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