A338009 Odd composite integers m such that A004254(m)^2 == 1 (mod m).

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

Table of n, a(n) for n=1..46.

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

Adjacent sequences: A338006 A338007 A338008 * A338010 A338011 A338012

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 06 2020

Status

approved