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A160542 Not divisible by 11.

%I A160542 #29 Jun 02 2025 01:41:35
%S A160542 1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,
%T A160542 29,30,31,32,34,35,36,37,38,39,40,41,42,43,45,46,47,48,49,50,51,52,53,
%U A160542 54,56,57,58,59,60,61,62,63,64,65,67,68,69,70,71,72,73,74,75,76,78,79,80,81,82,83,84,85,86,87,89,90,91,92,93,94,95,96,97,98,100,101,102,103,104,105,106,107,108,109,111,112
%N A160542 Not divisible by 11.
%C A160542 Contains numbers like 100, 111, 112, 113 which are not in A043096. - _R. J. Mathar_, May 20 2009
%H A160542 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).
%F A160542 a(n) = a(n-10) + 11, n>10. - _R. J. Mathar_, May 20 2009
%F A160542 G.f.: x*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10) / ( (1+x)*(1+x+x^2+x^3+x^4)*(x^4-x^3+x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, May 02 2014
%F A160542 Sum_{n>=1} (-1)^(n+1)/a(n) = (cot(Pi/11) - cot(2*Pi/11) + tan(Pi/22) - tan(3*Pi/22) + tan(5*Pi/22)) * Pi/11. - _Amiram Eldar_, May 11 2025
%p A160542 A160541 := proc(n)
%p A160542     option remember ;
%p A160542     if n <= 10 then
%p A160542         n;
%p A160542     else
%p A160542         procname(n-10)+11 ;;
%p A160542     end if;
%p A160542 end proc:
%p A160542 seq(A160541(n),n=1..100) ; # _R. J. Mathar_, Aug 05 2022
%t A160542 Select[Table[n,{n,200}],Mod[#,11]!=0&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2011 *)
%t A160542 LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{1,2,3,4,5,6,7,8,9,10,12},70] (* _Harvey P. Dale_, Sep 16 2020 *)
%o A160542 (Sage) [i for i in range(72) if gcd(11, i) == 1]
%Y A160542 Cf. A043096.
%K A160542 nonn,easy
%O A160542 1,2
%A A160542 _Zerinvary Lajos_, May 18 2009