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 A338010 Odd composite integers m such that A001109(m)^2 == 1 (mod m). 4
 9, 35, 51, 55, 77, 85, 119, 153, 169, 171, 187, 209, 261, 319, 369, 385, 451, 531, 551, 595, 649, 715, 741, 779, 899, 935, 961, 969, 989, 1105, 1121, 1189, 1241, 1309, 1443, 1469, 1479, 1711, 1829, 1989, 2001, 2047, 2091, 2261, 2345, 2419, 2555, 2849, 2915 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. This sequence satisfies the relation U(p)^2 == 1 for p prime and b=1,-1. The composite numbers with this property may be called weak generalized Lucas pseudoprimes of parameters a and b. The current sequence is defined for a=6 and b=1. REFERENCES D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020). LINKS Table of n, a(n) for n=1..49. D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021). MATHEMATICA Select[Range[3, 3000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3]*ChebyshevU[#-1, 3] - 1, #] &] CROSSREFS Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338009 (a=5, b=1), A338011 (a=7, b=1). Sequence in context: A003865 A265377 A187554 * A267702 A339995 A085366 Adjacent sequences: A338007 A338008 A338009 * A338011 A338012 A338013 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Oct 06 2020 STATUS approved

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)