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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 Table of n, a(n) for n=1..51. 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 Adjacent sequences: A338077 A338078 A338079 * A338081 A338082 A338083 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.)