A117522 Numbers k such that L(2*k + 1) is prime, where L(m) is a Lucas number.

2, 3, 5, 6, 8, 9, 15, 18, 20, 23, 26, 30, 35, 39, 56, 156, 176, 251, 306, 308, 431, 548, 680, 2393, 2396, 2925, 3870, 4233, 5345, 6125, 6981, 7224, 9734, 17724, 18389, 22253, 25584, 28001, 40835, 44924, 47411, 70028, 74045, 79760, 91544, 96600, 101333, 172146, 193716, 221804, 266138, 287109, 308393, 315590, 318875, 325910, 346073, 450828, 525924

Offset: 1

Author

Parthasarathy Nambi, Apr 26 2006

Keywords

• nonn
• hard

Comments

For n = 24..43, we can only claim that L(2*a(n) + 1) is a probable prime. Sequence arises in a study of A269254; for detailed theory, see [Hone]. - L. Edson Jeffery, Feb 09 2018

Examples

			If k = 56, then L(2*k + 1) is a prime with twenty-four digits.
		

Links

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

Crossrefs

Cf. A000032, A001606, A269251, A269252, A269253, A269254.

Cf. A294099, A298675, A298677, A298878, A299045, A299071, A285992, A299107, A299109, A088165, A299100, A299101, A113501.

Extensions

Values beyond 680 from L. Edson Jeffery, et al., Feb 02 2018

a(44)-a(56) from Robert Price, Jun 12 2025

a(57)-a(59) (using data in A001606) from Alois P. Heinz, Jun 12 2025