cp's OEIS Frontend

A229973 Numbers coprime to 39.

%I A229973 #24 Oct 23 2020 06:18:23
%S A229973 1,2,4,5,7,8,10,11,14,16,17,19,20,22,23,25,28,29,31,32,34,35,37,38,40,
%T A229973 41,43,44,46,47,49,50,53,55,56,58,59,61,62,64,67,68,70,71,73,74,76,77,
%U A229973 79,80,82,83,85,86,88,89,92,94,95,97,98,100,101,103,106
%N A229973 Numbers coprime to 39.
%C A229973 Numbers not divisible by 3 or 13.
%C A229973 For n from 1 to 24, a(n) mod 39-n - floor(11*n/25)-2*floor(n/8) has a period of 24, consisting of all zeros except a -2 at indices 8, 16, and 24.
%C A229973 The asymptotic density of this sequence is 8/13. - _Amiram Eldar_, Oct 23 2020
%H A229973 Vincenzo Librandi, <a href="/A229973/b229973.txt">Table of n, a(n) for n = 1..1000</a>
%H A229973 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1).
%F A229973 a(n+24) = a(n) + 39.
%F A229973 a(n) = 39*floor((n-1)/24) + f(n) + floor(11*f(n)/25) + 2*floor(f(n)/8) - 2*floor(((n-1)mod 8)/7) + 40*floor(f(n-1)/23), where f(n) = n mod 24.
%F A229973 G.f.: x*(x^22+x^20+x^18+x^16+2*x^14-x^12+3*x^11-x^10+2*x^8+x^6+x^4+x^2+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+1)*(x^4-x^2+1)*(x^4+1)*(x^8-x^4+1)). - _Colin Barker_, Oct 07 2013
%p A229973 for n from 1 to 50 do if n mod 3<>0 and n mod 13<>0 then print(n) fi od
%t A229973 CoefficientList[Series[(x^22 + x^20 + x^18 + x^16 + 2 x^14 - x^12 + 3 x^11 - x^10 + 2 x^8 + x^6 + x^4 + x^2 + 1)/((x - 1)^2 (x + 1) (x^2 - x + 1) (x^2 + 1) (x^4 - x^2 + 1) (x^4 + 1) (x^8 - x^4 + 1)), {x, 0, 80}], x] (* _Vincenzo Librandi_, Oct 08 2013 *)
%t A229973 Select[Range[100], CoprimeQ[39, #] &] (* _Amiram Eldar_, Oct 23 2020 *)
%Y A229973 Cf. A160545, A229829, A229968.
%K A229973 nonn,easy
%O A229973 1,2
%A A229973 _Gary Detlefs_, Oct 04 2013
%E A229973 More terms from _Colin Barker_, Oct 07 2013
%E A229973 a(34) corrected by _Vincenzo Librandi_, Oct 08 2013