Third-Order Recurrence Sequences with Infinitely Many Terms not Equal to the Sum of Two Prime Powers
Daniel Baczkowski and Bruce Keener
Department of Mathematics
The University of Findlay
1000 N. Main Street
Findlay, OH 45840
USA
Abstract:
We show in each of the Tribonacci, Padovan, Van der Laan, Perrin,
Leonardo, and Narayana's cows sequences that there are infinitely
many terms that cannot be represented as the sum of two prime powers.
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(Concerned with sequences
A000073
A000930
A000931
A001595
A001608.)
Received January 29 2026; revised version received March 19 2026.
Published in Journal of Integer Sequences,
March 24 2026.
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