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

Author

Ovidiu Bagdasar, Jun 17 2020

Keywords

• nonn

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.

Examples

			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.
		

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).

Crossrefs

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

Programs

Mathematica

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