The On-Line Encyclopedia of Integer Sequences (OEIS)

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A338010 revision #10

A338010

Odd composite integers m such that A001109(m)^2 == 1 (mod m).

9, 35, 51, 55, 77, 85, 119, 153, 169, 171, 187, 209, 261, 319, 369, 385, 451, 531, 551, 595, 649, 715, 741, 779, 899, 935, 961, 969, 989, 1105, 1121, 1189, 1241, 1309, 1443, 1469, 1479, 1711, 1829, 1989, 2001, 2047, 2091, 2261, 2345, 2419, 2555, 2849, 2915

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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=6 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..49.

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, 3000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3]*ChebyshevU[#-1, 3] - 1, #] &]

CROSSREFS

Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338009 (a=5, b=1), A338011 (a=7, b=1).

Sequence in context: A003865 A265377 A187554 * A267702 A339995 A085366

Adjacent sequences: A338007 A338008 A338009 * A338011 A338012 A338013

KEYWORD

nonn

AUTHOR

Ovidiu Bagdasar, Oct 06 2020

STATUS

proposed