A229968 - OEIS

%I #32 Oct 23 2020 03:28:43

%S 1,2,4,5,7,8,10,13,14,16,17,19,20,23,25,26,28,29,31,32,34,35,37,38,40,

%T 41,43,46,47,49,50,52,53,56,58,59,61,62,64,65,67,68,70,71,73,74,76,79,

%U 80,82,83,85,86,89,91,92,94,95,97,98,100,101,103,104,106

%N Numbers not divisible by 3 or 11.

%C Numbers coprime to 33.

%C For n from 1 to 20, a(n) mod 33 - n - floor(8*n/19) - 2*floor(n/7) has a period of 20 consisting of all zeros except for a -1 at index 7.

%C The first index where this differs from A192817 is n = 68; A192817(68) = 110 whereas a(68) = 112. - _Tom Edgar_, Feb 05 2015

%C The asymptotic density of this sequence is 20/33. - _Amiram Eldar_, Oct 23 2020

%H Vincenzo Librandi, <a href="/A229968/b229968.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

%F a(n+20) = a(n) + 33.

%F a(n) = 33*floor((n-1)/20) + f(n) + floor(8*f(n)/19) + 2*floor(f(n)/7) - floor(f(n+12)/19) + 32*floor(f(n-1)/19), where f(n) = n mod 20.

%F a(n) = a(n-1)+a(n-20)-a(n-21). G.f.: x*(x^20 +x^19 +2*x^18 +x^17 +2*x^16 +x^15 +2*x^14 +3*x^13 +x^12 +2*x^11 +x^10 +2*x^9 +x^8 +3*x^7 +2*x^6 +x^5 +2*x^4 +x^3 +2*x^2 +x +1) / ((x -1)^2*(x +1)*(x^2 +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)*(x^8 -x^6 +x^4 -x^2 +1)). - _Colin Barker_, Oct 08 2013

%p for n from 1 to 500 do if n mod 3<>0 and n mod 11 <>0 then print(n) fi od

%t Select[Range[132], GCD[#, 33] == 1 &] (* _Alonso del Arte_, Oct 05 2013 *)

%t Select[Range[200], Mod[#, 3]>0 && Mod[#, 11]>0 &] (* _Vincenzo Librandi_, Feb 08 2014 *)

%Y Cf. A007775, A192817.

%K nonn,easy

%O 1,2

%A _Gary Detlefs_, Oct 04 2013