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A306278 Numbers congruent to 2 or 11 mod 14.

%I A306278 #65 Jan 16 2023 18:38:44
%S A306278 2,11,16,25,30,39,44,53,58,67,72,81,86,95,100,109,114,123,128,137,142,
%T A306278 151,156,165,170,179,184,193,198,207,212,221,226,235,240,249,254,263,
%U A306278 268,277,282,291,296,305,310,319,324,333,338,347,352,361,366,375,380,389,394
%N A306278 Numbers congruent to 2 or 11 mod 14.
%H A306278 Colin Barker, <a href="/A306278/b306278.txt">Table of n, a(n) for n = 1..1000</a>
%H A306278 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A306278 a(n) = 7*n - A010703(n).
%F A306278 a(n) = 7*n - 4 + (-1)^n.
%F A306278 a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3.
%F A306278 A007310(a(n) + 1) = 7*A007310(n)
%F A306278 From _Jinyuan Wang_, Feb 03 2019: (Start)
%F A306278 For odd number k, a(k) = 7*k - 5.
%F A306278 For even number k, a(k) = 7*k - 3.
%F A306278 (End)
%F A306278 G.f.: x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)). - _Colin Barker_, Mar 14 2019
%F A306278 E.g.f.: 3 + (7*x - 4)*exp(x) + exp(-x). - _David Lovler_, Sep 07 2022
%p A306278 seq(seq(14*i+j, j=[2, 11]), i=0..28);
%t A306278 Flatten[Table[{14n + 2, 14n + 11}, {n, 0, 28}]]
%t A306278 LinearRecurrence[{1,1,-1},{2,11,16},60] (* _Harvey P. Dale_, Jan 16 2023 *)
%o A306278 (PARI) for(n=2, 394, if((n%14==2) || (n%14==11), print1(n, ", ")))
%o A306278 (PARI) for(n=1,57,print1(7*n-4+(-1)^n,", "))
%o A306278 (PARI) for(n=1,500,if(n%14==2,print1(n,", "));if(n%14==11,print1(n,", "))) \\ _Jinyuan Wang_, Feb 03 2019
%o A306278 (PARI) Vec(x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ _Colin Barker_, Mar 14 2019
%o A306278 (PARI) upto(n) = forstep(i = 2, n, [9, 5], print1(i", ")) \\ _David A. Corneth_, Mar 27 2019
%Y A306278 Cf. A007310, A010703, A020639, A047470, A091999, A273669, A306277, A306289.
%Y A306278 Primes greater than 2 in this sequence: A045471.
%K A306278 nonn,easy
%O A306278 1,1
%A A306278 _Davis Smith_, Feb 02 2019