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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 (list; graph; refs; listen; history; text; internal format)
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, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020)

D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021)

LINKS

Table of n, a(n) for n=1..51.

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

Adjacent sequences:  A337780 A337781 A337782 * A337784 A337785 A337786

KEYWORD

nonn

AUTHOR

Ovidiu Bagdasar, Sep 20 2020

EXTENSIONS

More terms from Amiram Eldar, Sep 21 2020

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)