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A338078
Odd composite integers m such that A085447(m) == 6 (mod m).
1
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
1,1
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)
MATHEMATICA
Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[LucasL[#, 6] - 6, #] &]
CROSSREFS
Cf. A006497, A005845 (a=1), A330276 (a=2), A335669 (a=3), A335670 (a=4), A335671 (a=5).
Sequence in context: A044389 A044770 A008877 * A376538 A336191 A277805
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 08 2020
EXTENSIONS
More terms from Amiram Eldar, Oct 09 2020
STATUS
approved