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A330206
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Chebyshev pseudoprimes to base 2: composite numbers k such that T(k, 2) == 2 (mod k), where T(k, x) is the k-th Chebyshev polynomial of the first kind.
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4
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209, 231, 399, 455, 901, 903, 923, 989, 1295, 1729, 1855, 2015, 2211, 2345, 2639, 2701, 2795, 2911, 3007, 3201, 3439, 3535, 3801, 4823, 5291, 5719, 6061, 6767, 6989, 7421, 8569, 9503, 9591, 9869, 10439, 10609, 11041, 11395, 11951, 11991, 13133, 13529, 13735, 13871
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OFFSET
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1,1
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COMMENTS
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Bang proved that T(p, a) == a (mod p) for every a > 0 and every odd prime. Rayes et al. (1999) defined Chebyshev pseudoprimes to base a as composite numbers k such that T(k, a) == a (mod k). They noted that the first Chebyshev pseudoprime to base 2 is 209.
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LINKS
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EXAMPLE
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209 is in the sequence since 209 = 11 * 19 is composite and T(209, 2) - 2 is divisible by 209.
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MATHEMATICA
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Select[Range[15000], CompositeQ[#] && Divisible[ChebyshevT[#, 2] - 2, #] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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