login
A338009
Odd composite integers m such that A004254(m)^2 == 1 (mod m).
4
25, 55, 115, 209, 253, 275, 319, 391, 425, 527, 551, 575, 713, 715, 775, 779, 935, 1105, 1111, 1265, 1705, 1807, 1919, 2015, 2035, 2071, 2575, 2627, 2893, 2915, 2929, 3281, 3289, 3655, 4031, 4033, 4141, 4199, 4355, 5191, 5291, 5671, 5699, 5777, 5885, 5983
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=5 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, 5985, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 5/2]*ChebyshevU[#-1, 5/2] - 1, #] &]
CROSSREFS
Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).
Sequence in context: A080863 A339729 A091214 * A036305 A370351 A257708
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 06 2020
STATUS
approved