Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Primes in Fibonacci n-step and Lucas n-step Sequences

Tony D. Noe
14025 NW Harvest Lane
Portland, OR 97229

Jonathan Vos Post
3225 North Marengo Avenue
Altadena, CA 91001

Abstract: 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.

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(Concerned with sequences A000032 A000045 A000073 A000078 A001591 A001592 A001605 A001606 A001644 A005478 A005479 A066178 A073817 A074048 A074584 A079262 A092835 A092836 A104534 A104535 A104576 A104577 A104621 A104622 A105753 A105754 A105755 A105756 A105757 A105758 A105759 A105760 A105761 A105762 A105763 A105764 A105765 A105766 A105767 and A105768.)

Received April 19 2005; revised version received September 2 2005. Published in Journal of Integer Sequences September 20 2005.

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