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%I #19 Nov 24 2023 12:39:30
%S 9,21,63,99,231,323,329,369,377,423,451,861,903,1081,1189,1443,1551,
%T 1819,1833,1869,1891,2033,2211,2737,2849,2871,2961,3059,3289,3653,
%U 3689,3827,4059,4089,4179,4181,4879,5671,5777,6447,6479,6601,6721,6903,7743
%N Odd composite integers m such that A001906(m)^2 == 1 (mod m).
%C For a, b integers, the generalized Lucas sequence is defined by the relation U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1.
%C This sequence satisfies the relation U(p)^2 == 1 for p prime and b=1,-1.
%C The composite numbers with this property may be called weak generalized Lucas pseudoprimes of parameters a and b.
%C The current sequence is defined for a=3 and b=1.
%D D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).
%H Dorin Andrica and Ovidiu Bagdasar, <a href="https://doi.org/10.3390/math9080838">On Generalized Lucas Pseudoprimality of Level k</a>, Mathematics (2021) Vol. 9, 838.
%H D. Andrica and O. Bagdasar, <a href="https://repository.derby.ac.uk/item/92yqq/on-some-new-arithmetic-properties-of-the-generalized-lucas-sequences">On some new arithmetic properties of the generalized Lucas sequences</a>, preprint for Mediterr. J. Math. 18, 47 (2021).
%t Select[Range[3, 8000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3/2]*ChebyshevU[#-1, 3/2] - 1, #] &]
%Y Cf. A338008 (a=4, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).
%K nonn
%O 1,1
%A _Ovidiu Bagdasar_, Oct 06 2020
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