allocated for Ovidiu BagdasarOdd composite integers m such that A001109(m)^2 == 1 (mod m).

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

1,1

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.

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)

Select[Range[3, 3000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3]*ChebyshevU[#-1, 3] - 1, #] &]

Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338009 (a=5, b=1), A338011 (a=7, b=1)

allocated

nonn

Ovidiu Bagdasar, Oct 06 2020

approved

editing

allocated for Ovidiu Bagdasar

allocated

approved