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%I #20 Nov 03 2018 18:47:17
%S 18,52,110,123,198,488,702,724,843,970,1298,1692,2158,2525,3330,4048,
%T 4862,5778,6726,6802,7940,9198,10084,10582,13752,15550,17498,19602,
%U 21868,24302,26910,29698,30248,32672,35838,39603,42770,46548,50542
%N Union_{odd primes p, n >= 3} {T_p(n)}, where T_m(x) = x*T_{m-1}(x) - T_{m-2}(x), m >= 2, T_0(x) = 2, T_1(x) = x (dilated Chebyshev polynomials of the first kind).
%C From a problem in A269254. For detailed theory, see [Hone].
%C Sequence avoids numbers of the form T_p(T_2(j)).
%H Andrew N. W. Hone, et al., <a href="https://arxiv.org/abs/1802.01793">On a family of sequences related to Chebyshev polynomials</a>, arXiv:1802.01793 [math.NT], 2018.
%t maxT = 55000; maxn = 12;
%t T[0][_] = 2; T[1][x_] = x;
%t T[m_][x_] := T[m][x] = x T[m-1][x] - T[m-2][x];
%t TT = Table[T[p][n], {p, Prime[Range[2, maxn]]}, {n, 3, Prime[maxn]}] // Flatten // Union // Select[#, # <= maxT&]&;
%t avoid = Table[T[p][T[2][n]], {p, Prime[Range[2, maxn]]}, {n, 3, Prime[maxn] }] // Flatten // Union // Select[#, # <= maxT&]&;
%t Complement[TT, avoid] (* _Jean-François Alcover_, Nov 03 2018 *)
%Y Cf. A008865 (T_2(n)), A298878 (T_p(n), p prime).
%Y Cf. A285992, A299107, A299109, A088165, A117522, A299100, A299101, A113501, A269253, A269254, A294099, A298675, A298677, A299045, A299071.
%K nonn
%O 1,1
%A _L. Edson Jeffery_, _Bob Selcoe_ and _Andrew Hone_, Feb 01 2018
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