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

Offset

1,1

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

Links

Table of n, a(n) for n=1..43.

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

Example

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

Crossrefs

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

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

Sequence in context: A173666 A063756 A358291 * A299101 A335658 A364807

Adjacent sequences: A117519 A117520 A117521 * A117523 A117524 A117525

Keyword

nonn,hard

Author

Parthasarathy Nambi, Apr 26 2006

Extensions

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

Status

approved