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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. 2
3, 5, 13, 89, 233, 1597, 2971215073 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 09:39 EST 2020. Contains 332011 sequences. (Running on oeis4.)