A338007 Odd composite integers m such that A001906(m)^2 == 1 (mod m).

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

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

Table of n, a(n) for n=1..45.

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

Adjacent sequences: A338004 A338005 A338006 * A338008 A338009 A338010

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 06 2020

Status

approved