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

Author

Ovidiu Bagdasar, Oct 22 2020

Keywords

• nonn

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)

Crossrefs

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

Programs

Mathematica

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

Extensions

More terms from Amiram Eldar, Oct 22 2020