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Not divisible by 11
7

%I #18 Jul 07 2023 12:42:19

%S 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 29,30,31,32,34,35,36,37,38,39,40,41,42,43,45,46,47,48,49,50,51,52,53,

%U 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 Not divisible by 11

%C Contains numbers like 100, 111, 112, 113 which are not in A043096. [_R. J. Mathar_, May 20 2009]

%H <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 a(n) = a(n-10) + 11, n>10. - _R. J. Mathar_, May 20 2009

%F 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

%p A160541 := proc(n)

%p option remember ;

%p if n <= 10 then

%p n;

%p else

%p procname(n-10)+11 ;;

%p end if;

%p end proc:

%p seq(A160541(n),n=1..100) ; # _R. J. Mathar_, Aug 05 2022

%t Select[Table[n,{n,200}],Mod[#,11]!=0&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2011*)

%t 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 (Sage) [i for i in range(72) if gcd(11, i) == 1]

%K nonn,easy

%O 1,2

%A _Zerinvary Lajos_, May 18 2009