A337236 Composite integers m such that A001076(m)^2 == 1 (mod m).

9, 63, 99, 119, 161, 207, 209, 231, 279, 323, 341, 377, 391, 549, 589, 671, 759, 779, 799, 897, 901, 1007, 1159, 1281, 1443, 1449, 1551, 1853, 1891, 2001, 2047, 2071, 2379, 2407, 2501, 2737, 2743, 2849, 2871, 2961, 3069, 3289, 3689, 3827, 4059, 4181, 4199, 4209, 4577

Offset

1,1

Comments

If p is a prime, then A001076(p)^2==1 (mod p).

This sequence contains the composite integers for which the congruence holds.

The generalized Lucas sequence of integer parameters (a,b) defined by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1, satisfies the identity U^2(p)==1 (mod p) whenever p is prime and b=-1,1.

For a=4, b=-1, U(n) recovers A001076(n).

References

D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 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, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 4]*Fibonacci[#, 4] - 1, #] &]

Crossrefs

Cf. A337231 (a=1, odd terms), A337232 (a=1, even terms), A337233 (a=2), A337234 (a=3, odd terms), A337235 (a=3, even terms).

Sequence in context: A159235 A181403 A292309 * A285456 A085645 A299579

Adjacent sequences: A337233 A337234 A337235 * A337237 A337238 A337239

Keyword

nonn

Author

Ovidiu Bagdasar, Aug 20 2020

Status

approved