A338078 Odd composite integers m such that A085447(m) == 6 (mod m).

57, 185, 385, 481, 629, 721, 779, 1121, 1441, 1729, 2419, 2737, 5665, 6721, 7471, 8401, 9361, 10465, 10561, 11285, 11521, 11859, 12257, 13585, 14705, 15281, 16321, 16583, 18849, 24721, 25345, 25441, 25593, 30745, 33649, 35219, 36481, 36581, 37949, 38665, 39169

Offset: 1

Author

Ovidiu Bagdasar, Oct 08 2020

Keywords

• nonn

Comments

If p is a prime, then A085447(p)==6 (mod p).

This sequence contains the odd 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, b=-1, V(m) recovers A085447(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. A006497, A005845 (a=1), A330276 (a=2), A335669 (a=3), A335670 (a=4), A335671 (a=5).

Programs

Mathematica

Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[LucasL[#, 6] - 6, #] &]

Extensions

More terms from Amiram Eldar, Oct 09 2020