A338011 Odd composite integers m such that A004187(m)^2 == 1 (mod m).

49, 161, 323, 329, 377, 451, 539, 989, 1081, 1127, 1189, 1771, 1819, 1891, 2009, 2033, 2047, 2303, 2737, 2849, 3059, 3289, 3619, 3653, 3689, 3827, 4181, 4301, 4577, 4879, 4949, 5671, 5777, 6049, 6479, 6533, 6601, 6721, 7061, 7399, 7471, 7567, 7931

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=7 and b=1.

References

D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020)

D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021)

Links

Table of n, a(n) for n=1..43.

Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.

Mathematica

Select[Range[3, 8000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 7/2]*ChebyshevU[#-1, 7/2] - 1, #] &]

Crossrefs

Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1).

Sequence in context: A265423 A226146 A339730 * A066551 A134210 A009409

Adjacent sequences: A338008 A338009 A338010 * A338012 A338013 A338014

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 06 2020

Status

approved