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%I #12 Nov 24 2023 12:39:40
%S 9,35,51,55,77,85,119,153,169,171,187,209,261,319,369,385,451,531,551,
%T 595,649,715,741,779,899,935,961,969,989,1105,1121,1189,1241,1309,
%U 1443,1469,1479,1711,1829,1989,2001,2047,2091,2261,2345,2419,2555,2849,2915
%N Odd composite integers m such that A001109(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=6 and b=1.
%D D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).
%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, 3000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3]*ChebyshevU[#-1, 3] - 1, #] &]
%Y Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338009 (a=5, b=1), A338011 (a=7, b=1).
%K nonn
%O 1,1
%A _Ovidiu Bagdasar_, Oct 06 2020
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