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A337781
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Odd composite integers m such that U(m)^2 == 1 (mod m) and V(m) == 7 (mod m), where U(m)=A004187(m) and V(m)=A056854(m) are the m-th generalized Lucas and Pell-Lucas numbers of parameters a=7 and b=1, respectively.
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2
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323, 329, 377, 451, 1081, 1189, 1819, 1891, 2033, 2737, 2849, 3059, 3289, 3653, 3689, 3827, 4181, 4879, 5671, 5777, 6479, 6601, 6721, 8149, 8533, 8557, 8569, 8651, 8701, 10199, 10877, 11309, 11339, 11521, 11663, 12341, 13201, 13489, 13861, 13981, 14701, 15251, 15301
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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=7 and b=1.
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LINKS
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MATHEMATICA
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Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 7/2] - 7, #] && Divisible[ChebyshevU[#-1, 7/2]*ChebyshevU[#-1, 7/2] - 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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