cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A338080 Odd composite integers such that A005668(m)^2 == 1 (mod m).

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%I A338080 #6 Oct 21 2020 23:07:34
%S A338080 9,57,63,143,171,247,323,399,407,481,629,703,721,779,899,927,1121,
%T A338080 1239,1407,1441,1463,1703,1729,2419,2529,2639,2737,3289,3367,3689,
%U A338080 4081,4847,4879,4921,5291,5339,5871,6061,6479,6489,6601,6721,6989,7067,7471,7859,8401,8911,8987,9139,9361
%N A338080 Odd composite integers such that A005668(m)^2 == 1 (mod m).
%C A338080 The generalized Lucas sequence of integer parameters (a,b) is defined by
%C A338080 U(m+2) = a*U(m+1)-b*U(m) and U(0)=0, U(1)=1.
%C A338080 Whenever p is prime and b=-1,1 we have U^2(p) == 1 (mod p).
%C A338080 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).
%D A338080 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020.
%D A338080 D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021)
%t A338080 Select[Range[3, 15000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 6]*Fibonacci[#, 6] - 1, #] &]
%Y A338080 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).
%K A338080 nonn
%O A338080 1,1
%A A338080 _Ovidiu Bagdasar_, Oct 08 2020