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A338011
Odd composite integers m such that A004187(m)^2 == 1 (mod m).
4
49, 161, 323, 329, 377, 451, 539, 989, 1081, 1127, 1189, 1771, 1819, 1891, 2009, 2033, 2047, 2303, 2737, 2849, 3059, 3289, 3619, 3653, 3689, 3827, 4181, 4301, 4577, 4879, 4949, 5671, 5777, 6049, 6479, 6533, 6601, 6721, 7061, 7399, 7471, 7567, 7931
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=7 and b=1.
REFERENCES
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)
LINKS
Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.
MATHEMATICA
Select[Range[3, 8000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 7/2]*ChebyshevU[#-1, 7/2] - 1, #] &]
CROSSREFS
Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1).
Sequence in context: A265423 A226146 A339730 * A066551 A134210 A009409
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 06 2020
STATUS
approved