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Displaying similar documents to “Palindromes in different bases: a conjecture of J. Ernest Wilkins.”

Counting Keith numbers.

Klazar, Martin, Luca, Florian (2007)

Journal of Integer Sequences [electronic only]

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Pseudoprime Cullen and Woodall numbers

Florian Luca, Igor E. Shparlinski (2007)

Colloquium Mathematicae

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We show that if a > 1 is any fixed integer, then for a sufficiently large x>1, the nth Cullen number Cₙ = n2ⁿ +1 is a base a pseudoprime only for at most O(x log log x/log x) positive integers n ≤ x. This complements a result of E. Heppner which asserts that Cₙ is prime for at most O(x/log x) of positive integers n ≤ x. We also prove a similar result concerning the pseudoprimality to base a of the Woodall numbers given by Wₙ = n2ⁿ - 1 for all n ≥ 1.