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A338007 Odd composite integers m such that A001906(m)^2 == 1 (mod m). 4
9, 21, 63, 99, 231, 323, 329, 369, 377, 423, 451, 861, 903, 1081, 1189, 1443, 1551, 1819, 1833, 1869, 1891, 2033, 2211, 2737, 2849, 2871, 2961, 3059, 3289, 3653, 3689, 3827, 4059, 4089, 4179, 4181, 4879, 5671, 5777, 6447, 6479, 6601, 6721, 6903, 7743 (list; graph; refs; listen; history; text; internal format)
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=3 and b=1.
REFERENCES
D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).
LINKS
Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.
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, 8000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3/2]*ChebyshevU[#-1, 3/2] - 1, #] &]
CROSSREFS
Cf. A338008 (a=4, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).
Sequence in context: A147337 A020290 A020288 * A147466 A262055 A193276
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 06 2020
STATUS
approved

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Last modified July 25 09:25 EDT 2024. Contains 374587 sequences. (Running on oeis4.)