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A338080 Odd composite integers such that A005668(m)^2 == 1 (mod m). 0
9, 57, 63, 143, 171, 247, 323, 399, 407, 481, 629, 703, 721, 779, 899, 927, 1121, 1239, 1407, 1441, 1463, 1703, 1729, 2419, 2529, 2639, 2737, 3289, 3367, 3689, 4081, 4847, 4879, 4921, 5291, 5339, 5871, 6061, 6479, 6489, 6601, 6721, 6989, 7067, 7471, 7859, 8401, 8911, 8987, 9139, 9361 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The generalized Lucas sequence of integer parameters (a,b) is defined by
U(m+2) = a*U(m+1)-b*U(m) and U(0)=0, U(1)=1.
Whenever p is prime and b=-1,1 we have U^2(p) == 1 (mod p).
Here we define the odd composite integers for which U^2(m) == 1 (mod m) holds, for a=6, b=-1, where U(m) is A005668(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
MATHEMATICA
Select[Range[3, 15000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 6]*Fibonacci[#, 6] - 1, #] &]
CROSSREFS
Cf. A337231 (a=1, odd terms), A337232 (a=1, even terms), A337233 (a=2), A337234 (a=3, odd terms), A337235 (a=3, even terms), A337236 (a=4), A337237 (a=5).
Sequence in context: A197530 A086888 A231315 * A064838 A027210 A192054
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 08 2020
STATUS
approved

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Last modified February 23 04:31 EST 2024. Contains 370267 sequences. (Running on oeis4.)