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A306279 Numbers congruent to 3 or 18 mod 22.

%I A306279 #64 Sep 09 2022 22:40:57
%S A306279 3,18,25,40,47,62,69,84,91,106,113,128,135,150,157,172,179,194,201,
%T A306279 216,223,238,245,260,267,282,289,304,311,326,333,348,355,370,377,392,
%U A306279 399,414,421,436,443,458,465,480,487,502,509,524,531,546,553,568
%N A306279 Numbers congruent to 3 or 18 mod 22.
%H A306279 Colin Barker, <a href="/A306279/b306279.txt">Table of n, a(n) for n = 1..1000</a>
%H A306279 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A306279 a(n) = 11*n - 6 + 2*(-1)^n.
%F A306279 a(n) = 11*n - A105398(n + 4).
%F A306279 A007310(a(n) + 1) = 11*A007310(n).
%F A306279 From _Colin Barker_, Feb 07 2019: (Start)
%F A306279 G.f.: x*(3 + 15*x + 4*x^2) / ((1 - x)^2*(1 + x)).
%F A306279 a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3. (End)
%F A306279 E.g.f.: 4 + (11*x - 6)*exp(x) + 2*exp(-x). - _David Lovler_, Sep 08 2022
%p A306279 seq(seq(22*i+j, j=[3, 18]), i=0..200);
%t A306279 Select[Range[200], MemberQ[{3, 18}, Mod[#, 22]] &]
%t A306279 Flatten[Table[{22n + 3, 22n + 18}, {n, 0, 43}]] (* _Alonso del Arte_, Feb 18 2019 *)
%o A306279 (PARI) for(n=3, 678, if((n%22==3) || (n%22==18), print1(n, ", ")))
%o A306279 (PARI) vector(62,n,11*n-6+2*(-1)^n)
%o A306279 (PARI) Vec(x*(3 + 15*x + 4*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ _Colin Barker_, Feb 07 2019
%o A306279 (Scala) (3 to 949 by 22).union(18 to 942 by 22).sorted // _Alonso del Arte_, Feb 18 2019
%Y A306279 Cf. A007310, A020639, A042948, A091999, A105398, A131555, A141850, A158459, A273669, A306277, A306289.
%Y A306279 Primes in this sequence: A141850.
%K A306279 nonn,easy
%O A306279 1,1
%A A306279 _Davis Smith_, Feb 02 2019