A299100 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.

1, 2, 3, 6, 9, 14, 18, 146, 216, 293, 704, 1143, 1530, 1593, 2924, 7163, 9176, 9489, 11531, 39543, 50423, 60720, 62868, 69993, 69995, 88103, 88163, 104606, 164441, 178551

Offset: 1

Author

L. Edson Jeffery, Bob Selcoe and Andrew Hone, Feb 02 2018

Keywords

• nonn
• hard
• more

Comments

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

a(31) > 2*10^5. - Robert Price, May 29 2020

Links

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

Crossrefs

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

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

Programs

Mathematica

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 *)

Extensions

a(24)-a(30) from Robert Price, May 29 2020