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

1,1

Comments

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).

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..48.

Mathematica

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

Crossrefs

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

Sequence in context: A090696 A048247 A276607 * A130442 A031073 A323151

Adjacent sequences: A338309 A338310 A338311 * A338313 A338314 A338315

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 22 2020

Status

approved