A299071 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).

18, 52, 110, 123, 198, 488, 702, 724, 843, 970, 1298, 1692, 2158, 2525, 3330, 4048, 4862, 5778, 6726, 6802, 7940, 9198, 10084, 10582, 13752, 15550, 17498, 19602, 21868, 24302, 26910, 29698, 30248, 32672, 35838, 39603, 42770, 46548, 50542

Offset

1,1

Comments

From a problem in A269254. For detailed theory, see [Hone].

Sequence avoids numbers of the form T_p(T_2(j)).

Links

Table of n, a(n) for n=1..39.

Andrew N. W. Hone, et al., On a family of sequences related to Chebyshev polynomials, arXiv:1802.01793 [math.NT], 2018.

Mathematica

maxT = 55000; maxn = 12;
T[0][_] = 2; T[1][x_] = x;
T[m_][x_] := T[m][x] = x T[m-1][x] - T[m-2][x];
TT = Table[T[p][n], {p, Prime[Range[2, maxn]]}, {n, 3, Prime[maxn]}] // Flatten // Union // Select[#, # <= maxT&]&;
avoid = Table[T[p][T[2][n]], {p, Prime[Range[2, maxn]]}, {n, 3, Prime[maxn] }] // Flatten // Union // Select[#, # <= maxT&]&;
Complement[TT, avoid] (* Jean-François Alcover, Nov 03 2018 *)

Crossrefs

Cf. A008865 (T_2(n)), A298878 (T_p(n), p prime).

Cf. A285992, A299107, A299109, A088165, A117522, A299100, A299101, A113501, A269253, A269254, A294099, A298675, A298677, A299045, A299071.

Sequence in context: A262454 A175815 A069130 * A124711 A126372 A334645

Adjacent sequences: A299068 A299069 A299070 * A299072 A299073 A299074

Keyword

nonn

Author

L. Edson Jeffery, Bob Selcoe and Andrew Hone, Feb 01 2018

Status

approved