A299107 Probable primes in sequence {s_k(4)}, where s_k(4) = 4*s_{k-1}(4) - s_{k-2}(4), k >= 2, s_0(4) = 1, s_1(4) = 5.

5, 19, 71, 3691, 191861, 138907099, 26947261171, 436315574686414344004975231616076636245689199862837798457639364993981991744926792179

Offset: 1

Author

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

Keywords

• nonn
• hard

Comments

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

Subsequent terms have too many digits to display.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..14
• Gary Greaves and Jose Yip, The coherent rank of a graph with three eigenvalues, arXiv:2406.17395 [math.CO], 2024. See p. 31.
• Andrew N. W. Hone, et al., On a family of sequences related to Chebyshev polynomials, arXiv:1802.01793 [math.NT], 2018.

Crossrefs

A269254, A001834, A294099 (row 4),

Cf. A285992, A299107, A299109, A088165, A117522, A299100, A299101, A113501, A269253, A298675, A298677, A298878, A299045, A299071, A086386.

Formula

a(n) = s_{A299100(n)}(4) = A001834(A299100(n)).