A338008 Odd composite integers m such that A001353(m)^2 == 1 (mod m).

35, 65, 91, 209, 455, 533, 595, 629, 679, 901, 923, 989, 1001, 1241, 1295, 1495, 1547, 1729, 1769, 1855, 1961, 1991, 2015, 2345, 2431, 2509, 2555, 2639, 2701, 2795, 2911, 3007, 3059, 3367, 3439, 3535, 3869, 3977, 4277, 4823, 5249, 5291, 5551, 5719, 5777

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=4 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.

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, 6000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 2]*ChebyshevU[#-1, 2] - 1, #] &]

Crossrefs

Cf. A338007 (a=3, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).

Sequence in context: A354502 A176875 A292005 * A331378 A331384 A297150

Adjacent sequences: A338005 A338006 A338007 * A338009 A338010 A338011

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 06 2020

Status

approved