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%I #18 Nov 24 2023 12:40:03
%S 25,55,115,209,253,275,319,391,425,527,551,575,713,715,775,779,935,
%T 1105,1111,1265,1705,1807,1919,2015,2035,2071,2575,2627,2893,2915,
%U 2929,3281,3289,3655,4031,4033,4141,4199,4355,5191,5291,5671,5699,5777,5885,5983
%N Odd composite integers m such that A004254(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=5 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, 5985, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 5/2]*ChebyshevU[#-1, 5/2] - 1, #] &]
%Y Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).
%K nonn
%O 1,1
%A _Ovidiu Bagdasar_, Oct 06 2020