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%I #56 Sep 09 2023 09:49:55
%S 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,
%T 27,28,29,30,31,32,3,34,35,36,37,38,39,40,41,42,43,4,45,46,47,48,49,
%U 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
%N a(n) = numerator(n/(n+11)).
%C 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
%C a(n) <> n iff n = 11 * k, in this case, a(n) = k. - _Bernard Schott_, Feb 19 2019
%H G. C. Greubel, <a href="/A106612/b106612.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,-1).
%F G.f.: x/(1-x)^2 - 10*x^11/(1-x^11)^2. - _Paul D. Hanna_, Jul 27 2005
%F a(n) = lcm(n,11)/11.
%F From _R. J. Mathar_, Apr 18 2011: (Start)
%F a(n) = A109052(n)/11.
%F Dirichlet g.f.: zeta(s-1)*(1-10/11^s). (End)
%F a(n) = 2*a(n-11) - a(n-22). - _G. C. Greubel_, Feb 19 2019
%F From _Amiram Eldar_, Nov 25 2022: (Start)
%F Multiplicative with a(11^e) = 11^(e-1), and a(p^e) = p^e if p != 11.
%F Sum_{k=1..n} a(k) ~ (111/242) * n^2. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 21*log(2)/11. - _Amiram Eldar_, Sep 08 2023
%p seq(numer(n/(n+11)),n=0..80); # _Muniru A Asiru_, Feb 19 2019
%t f[n_]:=Numerator[n/(n+11)];Array[f,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011 *)
%t 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 *)
%o (Sage) [lcm(n,11)/11 for n in range(0, 54)] # _Zerinvary Lajos_, Jun 09 2009
%o (Magma) [Numerator(n/(n+11)): n in [0..100]]; // _Vincenzo Librandi_, Apr 18 2011
%o (PARI) vector(100, n, n--; numerator(n/(n+11))) \\ _G. C. Greubel_, Feb 19 2019
%o (GAP) List([0..80],n->NumeratorRat(n/(n+11))); # _Muniru A Asiru_, Feb 19 2019
%Y Cf. A109052, A137564 (differs, e.g., for n=100).
%Y Cf. Sequences given by the formula numerator(n/(n + k)): A026741 (k = 2), A051176 (k = 3), A060819 (k = 4), A060791 (k = 5), A060789 (k = 6), A106608 thru A106611 (k = 7 thru 10), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20).
%K nonn,frac,mult,easy
%O 0,3
%A _N. J. A. Sloane_, May 15 2005
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