Geodesic
Primes in Fibonacci \(n\)-step and Lucas \(n\)-step sequences
Journal of integer sequences, Tome 8 (2005) no. 4
We search for primes in the Fibonacci $n$-step and Lucas $n$-step sequences, which are the natural generalizations of the Fibonacci and Lucas numbers. While the Fibonacci $n$-step sequences are nearly devoid of primes, the Lucas $n$-step sequences are prime-rich. We tabulate the occurrence of primes in the first 10000 terms for $n = 100$. We also state two conjectures about Diophantine equations based on these sequences.
Keywords: prime numbers, generalized Fibonacci and Lucas numbers 
@article{JIS_2005__8_4_a5,
     author = {Noe,  Tony D. and Vos Post,  Jonathan},
     title = {Primes in {Fibonacci} \(n\)-step and {Lucas} \(n\)-step sequences},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {4},
     zbl = {1101.11008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a5/}
}
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Noe,  Tony D.; Vos Post,  Jonathan. Primes in Fibonacci \(n\)-step and Lucas \(n\)-step sequences. Journal of integer sequences, Tome 8 (2005) no. 4. http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a5/