A338310 Even composites m such that A086902(m)==7 (mod m).

4, 8, 22, 88, 472, 5588, 10408, 20648, 34568, 123076, 1783976, 3677228, 4609418, 4857688, 6027208, 9906578, 16508152, 19995308, 20226572, 32039062, 56484004, 88835528, 97896692, 135858088, 354671468, 1091638108, 2260976428, 3495804596, 3723523516, 5577624308

Offset

1,1

Comments

If p is a prime, then A086902(p)==7 (mod p).

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

The generalized Pell-Lucas sequence of integer parameters (a,b) defined by V(m+2)=a*V(m+1)-b*V(m) and V(0)=2, V(1)=a, satisfy the identity V(p)==a (mod p) whenever p is prime and b=-1,1.

For a=7, b=-1, V(m) recovers A086902(m).

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..30.

Mathematica

Select[Range[2, 25000, 2], CompositeQ[#] && Divisible[LucasL[#, 7] - 7, #] &]

Crossrefs

Cf. A338079 (sequence of odd terms); A335668 (a=2).

Sequence in context: A129788 A170938 A003684 * A254404 A254403 A075688

Adjacent sequences: A338307 A338308 A338309 * A338311 A338312 A338313

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 22 2020

Extensions

a(9)-a(15) from Amiram Eldar, Oct 22 2020

a(16)-a(30) from Daniel Suteu, Oct 22 2020

Status

approved