A299100 - OEIS

%I #31 May 29 2020 20:41:40

%S 1,2,3,6,9,14,18,146,216,293,704,1143,1530,1593,2924,7163,9176,9489,

%T 11531,39543,50423,60720,62868,69993,69995,88103,88163,104606,164441,

%U 178551

%N Indices k such that s_k(4) is a (probable) prime, where s_k(4) = 4*s_{k-1}(4) - s_{k-2}(4), k >= 2, s_0(4) = 1, s_1(4) = 5.

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

%C a(31) > 2*10^5. - _Robert Price_, May 29 2020

%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 s[k_, m_] := s[k, m] = Which[k == 0, 1, k == 1, 1 + m, True, m s[k - 1, m] - s[k - 2, m]]; Select[Range@ 2000, PrimeQ@ Abs@ s[#, 4] &] (* _Michael De Vlieger_, Feb 03 2018 *)

%Y Cf. A269254. Indices of primes in A001834, A294099 (row 4).

%Y Cf. A285992, A299107, A299109, A088165, A117522, A299100, A299101, A113501, A269253, A298675, A298677, A298878, A299045, A299071.

%K nonn,hard,more

%O 1,2

%A _L. Edson Jeffery_, _Bob Selcoe_ and _Andrew Hone_, Feb 02 2018

%E a(24)-a(30) from _Robert Price_, May 29 2020