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%I #42 Jul 16 2022 18:47:57
%S 2,3,8,9,14,15,20,21,26,27,32,33,38,39,44,45,50,51,56,57,62,63,68,69,
%T 74,75,80,81,86,87,92,93,98,99,104,105,110,111,116,117,122,123,128,
%U 129,134,135,140,141,146,147,152,153,158,159,164,165,170,171,176,177,182,183
%N Numbers that are congruent to {2, 3} mod 6.
%C Solutions to 3^x - 2^x == 5 (mod 7). - _Cino Hilliard_, May 09 2003
%D Emil Grosswald, Topics From the Theory of Numbers, 1966, p. 65, problem 23.
%H Michael De Vlieger, <a href="/A047243/b047243.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 6*n - 7 - a(n-1), with a(1)=2. - _Vincenzo Librandi_, Aug 05 2010
%F G.f.: x*(2+x+3*x^2) / ( (1+x)*(1-x)^2 ). - _R. J. Mathar_, Oct 08 2011
%F From _Guenther Schrack_, Jun 21 2019: (Start)
%F a(n) = a(n-2) + 6 with a(1)=2, a(2)=3 for n > 2;
%F a(n) = 3*n - 2 - (-1)^n. (End)
%F E.g.f.: 3 - 3*(1-x)*cosh(x) - (1-3*x)*sinh(x). - _G. C. Greubel_, Jun 30 2019
%F E.g.f.: 3 + (3*x-3)*exp(x) + 2*sinh(x). - _David Lovler_, Jul 16 2022
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(12*sqrt(3)) + log(3)/4 - log(2)/3. - _Amiram Eldar_, Dec 13 2021
%t Select[Range[0, 210], MemberQ[{2, 3}, Mod[#, 6]] &] (* or *)
%t Fold[Append[#1, 6 #2 - Last@ #1 - 7] &, {2}, Range[2, 70]] (* or *)
%t Rest@ CoefficientList[Series[x(2+x+3x^2)/((1+x)(1-x)^2), {x, 0, 70}], x] (* _Michael De Vlieger_, Jan 12 2018 *)
%o (PARI) vector(70, n, 3*n-2-(-1)^n) \\ _G. C. Greubel_, Jun 30 2019
%o (Magma) [3*n-2-(-1)^n: n in [1..70]]; // _G. C. Greubel_, Jun 30 2019
%o (Sage) [3*n-2-(-1)^n for n in (1..70)] # _G. C. Greubel_, Jun 30 2019
%o (GAP) List([1..70], n-> 3*n-2-(-1)^n) # _G. C. Greubel_, Jun 30 2019
%Y Cf. A030531. Complement of A047260.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Cino Hilliard_, May 09 2003
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