A121533 Fibonacci-Lucas prime twins: Prime Fibonacci numbers Fibonacci(k) such that Lucas numbers Lucas(k) = Fibonacci(k-1) + Fibonacci(k+1) are also prime.

3, 5, 13, 89, 233, 1597, 2971215073

Offset

1,1

Comments

Indices for Fibonacci-Lucas prime twins are A080327(n) = {4, 5, 7, 11, 13, 17, 47, ...}. Corresponding Lucas-Fibonacci prime twins are A121534(n) = {7, 11, 29, 199, 521, 3571, 6643838879, ...}. Probable primes Fibonacci(148091) and Lucas(148091) are the next probable Fibonacci-Lucas and Lucas-Fibonacci prime twins. They have 30949 and 30950 digits.

Links

Table of n, a(n) for n=1..7.

Example

a(1) = 3 because Fibonacci(4) = 3 is prime and Lucas(4) = 5 is also prime.

Mathematica

Do[f=Fibonacci[n]; l=Fibonacci[n-1]+Fibonacci[n+1]; If[PrimeQ[f]&&PrimeQ[l], Print[{f, l}]], {n, 10000}]

Crossrefs

Cf. A121534, A000045, A005478, A001605, A001606, A000032, A000204, A005479, A080327.

Sequence in context: A180313 A053630 A155012 * A187733 A087170 A123370

Adjacent sequences: A121530 A121531 A121532 * A121534 A121535 A121536

Keyword

nonn

Author

Alexander Adamchuk, Aug 05 2006

Status

approved