A271429 Primes of the form L(k)*L(k+1)-1, where L(k) is the k-th Lucas number (A000032).

2, 11, 197, 521, 3571, 20633237, 54018521, 370248451, 119218851371, 5600748293801, 10420180999117162547, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Example

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

Mathematica

Array[LucasL@ # LucasL[# + 1] - 1 &, {160}] /. n_ /; CompositeQ@ n -> Nothing (* Michael De Vlieger, Apr 07 2016 *)
Select[Times@@@Partition[LucasL[Range[200]], 2, 1]-1, PrimeQ] (* Harvey P. Dale, May 14 2020 *)

Prog

(PARI)
lucas(n) = fibonacci(n+1) + fibonacci(n-1)
L=List(); for(k=1, 200, if(isprime(p=lucas(k)*lucas(k+1)-1), listput(L, p))); Vec(L)

Crossrefs

Cf. A000032, A271430.

Sequence in context: A132871 A140314 A226052 * A051663 A348859 A358649

Adjacent sequences: A271426 A271427 A271428 * A271430 A271431 A271432

Keyword

nonn

Author

Colin Barker, Apr 07 2016

Status

approved