A338311 Even composites m such that A003499(m)==6 (mod m).

4, 14, 28, 164, 434, 574, 1106, 5084, 5572, 7874, 8386, 13454, 13694, 19964, 21988, 33166, 39934, 40132, 95122, 103886, 113918, 148994, 157604, 215326, 216124, 256004, 277564, 306404, 341342, 366148, 571154, 660674, 662494, 764956, 771374, 876644, 981646, 1070926

Offset

1,1

Comments

If p is a prime, then A003499(p)==6 (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=6 and b=1, V(m) recovers A003499(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..38.

Mathematica

Select[Range[2, 25000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 3] - 6, #] &]

Crossrefs

Cf. A337233 (sequence of odd terms), A337777 (a=3).

Sequence in context: A033690 A316213 A296985 * A244714 A218212 A305637

Adjacent sequences: A338308 A338309 A338310 * A338312 A338313 A338314

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 22 2020

Extensions

More terms from Amiram Eldar, Oct 22 2020

Status

approved