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A337783
Even composite integers m such that U(m)^2 == 1 (mod m), where U(m)=A004187(m) is the m-th generalized Lucas number of parameters a=7 and b=1.
1
4, 8, 16, 44, 104, 136, 152, 164, 176, 232, 286, 442, 496, 656, 836, 856, 976, 1072, 1364, 1378, 1394, 1804, 1826, 2204, 2248, 2584, 2626, 2684, 2834, 3016, 3268, 3536, 3926, 4264, 4346, 4636, 5084, 5104, 5146, 5662, 7208, 7216, 7384, 7676, 7964, 8294, 8632, 8774, 9164, 9316, 9976
OFFSET
1,1
COMMENTS
This sequence contains the even composite integers for which the congruence holds.
The generalized Lucas sequences of integer parameters (a,b) defined by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1, satisfies the identity U^(p)==1 (mod p) whenever p is prime and b=-1,1.
REFERENCES
D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 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[2, 10000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 7/2]*ChebyshevU[#-1, 7/2] - 1, #] &]
CROSSREFS
Cf. A337781 and A337782.
Sequence in context: A065605 A065978 A077447 * A301773 A102358 A038238
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Sep 20 2020
EXTENSIONS
More terms from Amiram Eldar, Sep 21 2020
STATUS
approved