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A338310
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Even composites m such that A086902(m)==7 (mod m).
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0
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4, 8, 22, 88, 472, 5588, 10408, 20648, 34568, 123076, 1783976, 3677228, 4609418, 4857688, 6027208, 9906578, 16508152, 19995308, 20226572, 32039062, 56484004, 88835528, 97896692, 135858088, 354671468, 1091638108, 2260976428, 3495804596, 3723523516, 5577624308
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OFFSET
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1,1
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COMMENTS
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If p is a prime, then A086902(p)==7 (mod p).
This sequence contains the even composite integers for which the congruence holds.
The generalized Pell-Lucas sequence of integer parameters (a,b) defined by V(m+2)=a*V(m+1)-b*V(m) and V(0)=2, V(1)=a, satisfy the identity V(p)==a (mod p) whenever p is prime and b=-1,1.
For a=7, b=-1, V(m) recovers A086902(m).
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REFERENCES
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D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020)
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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MATHEMATICA
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Select[Range[2, 25000, 2], CompositeQ[#] && Divisible[LucasL[#, 7] - 7, #] &]
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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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