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A338008
Odd composite integers m such that A001353(m)^2 == 1 (mod m).
4
35, 65, 91, 209, 455, 533, 595, 629, 679, 901, 923, 989, 1001, 1241, 1295, 1495, 1547, 1729, 1769, 1855, 1961, 1991, 2015, 2345, 2431, 2509, 2555, 2639, 2701, 2795, 2911, 3007, 3059, 3367, 3439, 3535, 3869, 3977, 4277, 4823, 5249, 5291, 5551, 5719, 5777
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=4 and b=1.
REFERENCES
D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).
LINKS
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, 6000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 2]*ChebyshevU[#-1, 2] - 1, #] &]
CROSSREFS
Cf. A338007 (a=3, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).
Sequence in context: A354502 A176875 A292005 * A331378 A331384 A297150
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 06 2020
STATUS
approved