A338311 -id:A338311 - cp's OEIS frontend

A338312 Even composites m such that A056854(m)==7 (mod m).

4, 8, 10, 20, 40, 44, 104, 136, 152, 170, 190, 232, 260, 286, 442, 580, 740, 836, 890, 1364, 1378, 1990, 2204, 2260, 2584, 2626, 2684, 2834, 3016, 3160, 3230, 3926, 4220, 4636, 5662, 6290, 7208, 7384, 7540, 7676, 7964, 8294, 8420, 9164, 9316, 9320, 10070, 11476

Offset: 1

Ovidiu Bagdasar, Oct 22 2020

nonn

If p is a prime, then A056854(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 and b=1, V(m) recovers A056854(m).

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)

Cf. A338082 (sequence of odd terms), A337777 (a=3), A338311 (a=6).

Select[Range[2, 20000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 7/2] - 7, #] &]

cp's OEIS Frontend

A338312 Even composites m such that A056854(m)==7 (mod m).

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