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A338008
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Odd composite integers m such that A001353(m)^2 == 1 (mod m).
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4
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35, 65, 91, 209, 455, 533, 595, 629, 679, 901, 923, 989, 1001, 1241, 1295, 1495, 1547, 1729, 1769, 1855, 1961, 1991, 2015, 2345, 2431, 2509, 2555, 2639, 2701, 2795, 2911, 3007, 3059, 3367, 3439, 3535, 3869, 3977, 4277, 4823, 5249, 5291, 5551, 5719, 5777
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OFFSET
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1,1
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COMMENTS
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For a, b integers, the generalized Lucas sequence is defined by the relation U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1.
This sequence satisfies the relation U(p)^2 == 1 for p prime and b=1,-1.
The composite numbers with this property may be called weak generalized Lucas pseudoprimes of parameters a and b.
The current sequence is defined for a=4 and b=1.
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REFERENCES
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D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).
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LINKS
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MATHEMATICA
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Select[Range[3, 6000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 2]*ChebyshevU[#-1, 2] - 1, #] &]
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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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