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A337629
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Odd composite integers m such that U(m)^2 == 1 (mod m) and V(m) == 6 (mod m), where U(m) and V(m) are the m-th generalized Lucas and Pell-Lucas numbers of parameters a=6 and b=-1, respectively.
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2
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57, 481, 629, 721, 779, 1121, 1441, 1729, 2419, 2737, 6721, 7471, 8401, 9361, 10561, 11521, 11859, 12257, 15281, 16321, 16583, 18849, 24721, 25441, 25593, 33649, 35219, 36481, 36581, 37949, 39169, 41041, 45961, 46999, 50681, 52417, 53041, 53521, 54757, 55537
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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=6 and b=-1.
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REFERENCES
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D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021)
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LINKS
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Table of n, a(n) for n=1..40.
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MATHEMATICA
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Select[Range[3, 15000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 6]*Fibonacci[#, 6] - 1, #] && Divisible[LucasL[#, 6] - 6, #] &]
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CROSSREFS
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Cf. A337625 (a=1), A337626 (a=3), A337627 (a=4), A337628 (a=5).
Sequence in context: A076459 A268260 A184224 * A218812 A290779 A027143
Adjacent sequences: A337626 A337627 A337628 * A337630 A337631 A337632
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KEYWORD
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nonn
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AUTHOR
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Ovidiu Bagdasar, Sep 19 2020
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EXTENSIONS
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More terms from Amiram Eldar, Sep 19 2020
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STATUS
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approved
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