A335668 Even composites m such that A002203(m) == 2 (mod m).

4, 8, 16, 24, 32, 48, 64, 72, 96, 120, 128, 144, 168, 192, 216, 240, 256, 264, 272, 288, 336, 360, 384, 432, 480, 504, 512, 528, 544, 576, 600, 648, 672, 720, 768, 792, 816, 840, 864, 960, 1008, 1024, 1056, 1080, 1088, 1152, 1176, 1200, 1296, 1320, 1344, 1440, 1512

Offset

1,1

Comments

If p is a prime, then A002203(p)==2 (mod p).

Even composites for which the congruence holds.

Even composites m for which the sum of the Pell numbers A000129(0) + ... + A000129(m-1) is divisible by m.

References

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).

Example

4 is the first composite number m for which A002203(m)==2 (mod m) since A002203(4)=34==2 (mod 4), so a(1)=4.
The next even composite for which the congruence holds is m = 8 since A002203(8)=1154==2 (mod 8), so a(2)=8.

Mathematica

Select[Range[4, 2000, 2], Divisible[LucasL[#, 2] - 2, #] &] (* Amiram Eldar, Jun 18 2020 *)

Crossrefs

Cf. A270342 (all positive integers), A270345 (all composites), A330276 (odd composites),

Sequence in context: A160746 A160740 A270345 * A181823 A308985 A046059

Adjacent sequences: A335665 A335666 A335667 * A335669 A335670 A335671

Keyword

nonn

Author

Ovidiu Bagdasar, Jun 17 2020

Status

approved