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A146509 Numbers that are congruent to {1, 5} mod 18.

%I A146509 #50 Oct 03 2024 23:26:37
%S A146509 1,5,19,23,37,41,55,59,73,77,91,95,109,113,127,131,145,149,163,167,
%T A146509 181,185,199,203,217,221,235,239,253,257,271,275,289,293,307,311,325,
%U A146509 329,343,347,361,365,379,383,397,401,415,419,433,437,451,455,469,473,487
%N A146509 Numbers that are congruent to {1, 5} mod 18.
%C A146509 Positive integers k such that Hypergeometric[k/6,(6-k)/6,1/2,3/4] = 2Cos[2Pi/9].
%H A146509 Vincenzo Librandi, <a href="/A146509/b146509.txt">Table of n, a(n) for n = 1..1000</a>
%H A146509 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A146509 a(2k-1) = 18*(k-1)+1, a(2k) = 18*(k-1)+5, where k>0.
%F A146509 G.f.: x*(1+4*x+13*x^2)/((1+x)*(1-x)^2). - _Vincenzo Librandi_, Jul 11 2012
%F A146509 a(n) = (18*n - 5*(-1)^n - 21)/2. - _Bruno Berselli_, Jul 12 2012 [Corrected by _David Lovler_, Sep 24 2022]
%F A146509 a(1)=1, a(n) = 18*n -a(n-1) -30. - _Vincenzo Librandi_, Jul 12 2012
%F A146509 E.g.f.: 13 + ((18*x - 21)*exp(x) - 5*exp(-x))/2. - _David Lovler_, Sep 05 2022
%t A146509 Select[Range[500],MemberQ[{1,5},Mod[#,18]]&] (* _Harvey P. Dale_, Jul 24 2011 *)
%o A146509 (Magma) [n: n in [1..500] | n mod 18 in [1,5]]; // _Bruno Berselli_, Jul 12 2012
%o A146509 (PARI) a(n)=n\2*18+if(n%2,1,-13) \\ _Charles R Greathouse IV_, Jul 14 2012
%Y A146509 Cf. A146507, A146511, A146512.
%K A146509 nonn,easy
%O A146509 1,2
%A A146509 _Artur Jasinski_, Oct 30 2008
%E A146509 Crossrefs corrected by _Ray Chandler_, Dec 06 2016