A271430 Values of k such that L(k)*L(k+1)-1 is a prime, where L(k) is the k-th Lucas number (A000032).

1, 2, 5, 6, 8, 17, 18, 20, 26, 30, 45, 56, 156, 176, 306, 308, 548, 680, 1197, 2393, 2396, 3870, 4397, 7224, 9734, 17724, 25584, 31793, 44924, 70028, 79760, 91544, 96600

Offset

1,2

Comments

a(34) > 10^5. - Robert Price, Apr 17 2016

Links

Table of n, a(n) for n=1..33.

Example

2 is in the sequence because L(2)*L(3)-1 = 3*4-1 = 11, which is prime.

Mathematica

Select[Range@ 5000, PrimeQ[LucasL@ # LucasL[# + 1] - 1] &] (* Michael De Vlieger, Apr 07 2016 *)

Prog

(PARI)
lucas(n) = fibonacci(n+1) + fibonacci(n-1)
L=List(); for(k=1, 1000, if(ispseudoprime(lucas(k)*lucas(k+1)-1), listput(L, k))); Vec(L)

Crossrefs

Cf. A000032, A271429.

Sequence in context: A079256 A191204 A191140 * A326854 A097685 A136369

Adjacent sequences: A271427 A271428 A271429 * A271431 A271432 A271433

Keyword

nonn,more

Author

Colin Barker, Apr 07 2016

Extensions

a(22)-a(33) from Robert Price, Apr 17 2016

Status

approved