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A337626
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Odd composite integers m such that U(m)^2 == 1 (mod m) and V(m) == 3 (mod m), where U(m) and V(m) are the m-th generalized Lucas and Pell-Lucas numbers of parameters a=3 and b=-1, respectively.
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5
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33, 119, 385, 561, 649, 1189, 1441, 2065, 2289, 2465, 2849, 4187, 6545, 12871, 13281, 14041, 16109, 18241, 22049, 23479, 24769, 25345, 28421, 31631, 34997, 38121, 38503, 41441, 45961, 48577, 50545, 53585, 56279, 58081, 59081, 61447, 63393, 66385, 75077, 91187
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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 following sequences are defined:
generalized Lucas sequences by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1,
generalized Pell-Lucas sequences by V(n+2)=a*V(n+1)-b*V(n) and V(0)=2, V(1)=a.
These satisfy the identities U(p)^2 == 1 and V(p)==a (mod p) for p prime and b=1,-1.
These numbers may be called weak generalized Lucas-Bruckner pseudoprimes of parameters a and b.The current sequence is defined for a=3 and b=-1.
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LINKS
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MATHEMATICA
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Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 3]*Fibonacci[#, 3] - 1, #] && Divisible[LucasL[#, 3] - 3, #] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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