Search: id:A121534
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%I A121534
%S A121534 5,11,29,199,521,3571,6643838879
%N A121534 Lucas-Fibonacci prime twins: Prime Lucas numbers L[k] such that Fibonacci 
               numbers F[k] are prime too.
%C A121534 Indices for Lucas-Fibonacci prime twins are A080327[n] = {4,5,7,11,13,
               17,47,...}. Corresponding Fibonacci-Lucas prime twins are A121533[n] 
               = {3,5,13,89,233,1597,2971215073,...}. Probable primes Fibonacci[148091] 
               and Lucas[148091] are the next probable Fibonacci-Lucas and Lucas-Fibonacci 
               prime twins. They have 30949 and 30950 digits.
%C A121534 General recurrence is a(n)=(a(1)-1)*a(n-1)-a(n-2), a(1)>=4, lim n->infinity 
               a(n)= x*(k*x+1)^n, k =(a(1)-3), x=(1+sqrt((a(1)+1)/(a(1)-3)))/2. 
               Examples in OEIS: a(1)=4 gives A002878, primes in it A121534. a(1)=5 
               gives A001834, primes in it A086386. a(1)=6 gives A030221, primes 
               in it not in OEIS {29,139,3191,...}. a(1)=7 gives A002315, primes 
               in it A088165. a(1)=8 gives A033890, primes in it not in OEIS (does 
               there exist any ?). a(1)=9 gives A057080, primes in it not in OEIS 
               {71,34649,16908641,...}. a(1)=10 gives A057081, primes in it not 
               in OEIS {389806471,192097408520951,...}. [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), 
               Sep 02 2008]
%e A121534 a(1) = 5 because Lucas[4] = 5 is prime and Fibonacci[4] = 3 is prime 
               too.
%t A121534 Do[f=Fibonacci[n]; l=Fibonacci[n-1]+Fibonacci[n+1]; If[PrimeQ[f]&&PrimeQ[l], 
               Print[{f,l}]], {n,10000}]
%Y A121534 Cf. A121534, A121535, A000045, A005478, A001605, A001606, A000032, A000204, 
               A005479, A080327.
%Y A121534 Sequence in context: A100965 A001632 A053185 this_sequence A090119 A088484 
               A114688
%Y A121534 Adjacent sequences: A121531 A121532 A121533 this_sequence A121535 A121536 
               A121537
%K A121534 nonn
%O A121534 1,1
%A A121534 Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 05 2006

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