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A337779
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Odd composite integers m such that U(m)^2 == 1 (mod m) and V(m) == 5 (mod m), where U(m)=A004254(m) and V(m)=A003501(m) are the m-th generalized Lucas and Pell-Lucas numbers of parameters a=5 and b=1, respectively.
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3
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527, 551, 1105, 1807, 1919, 2015, 2071, 2915, 3289, 4031, 4033, 4355, 5291, 5777, 5983, 6049, 6061, 6479, 6785, 7645, 8695, 9361, 9889, 11285, 11663, 11951, 12209, 12265, 12545, 13079, 14491, 16211, 17119, 17249, 18299, 18407, 20087, 20099, 20845, 21505, 22499
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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=5 and b=1.
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LINKS
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MATHEMATICA
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Select[Range[3, 10000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 5/2] - 5, #] && Divisible[ChebyshevU[#-1, 5/2]*ChebyshevU[#-1, 5/2] - 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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EXTENSIONS
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STATUS
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approved
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