The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A337231 Odd composite integers m such that F(m)^2 == 1 (mod m), where F(m) is the m-th Fibonacci number. 11
 231, 323, 377, 1443, 1551, 1891, 2737, 2849, 3289, 3689, 3827, 4181, 4879, 5777, 6479, 6601, 6721, 7743, 8149, 9879, 10877, 11663, 13201, 13981, 15251, 15301, 17119, 17261, 17711, 18407, 19043, 20999, 23407, 25877, 27071, 27323, 29281, 30889, 34561, 34943, 35207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is a prime, then A000045(p)^2==1 (mod p). This sequence contains the odd composite integers for which the congruence holds. The generalized Lucas sequence of integer parameters (a,b) defined by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1, satisfies the identity U^2(p)==1 (mod p) whenever p is prime and b=-1. For a=1, b=-1, U(n) recovers A000045(n) (Fibonacci numbers). REFERENCES D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020). LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838. D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021). MATHEMATICA Select[Range[3, 30000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 1]*Fibonacci[#, 1] - 1, #] &] PROG (PARI) lista(nn) = my(list=List()); forcomposite(c=1, nn, if ((c%2) && (Mod(fibonacci(c), c)^2 == 1), listput(list, c))); Vec(list); \\ Michel Marcus, Sep 29 2023 CROSSREFS Cf. A000045. Sequence in context: A088289 A046009 A350367 * A117223 A160355 A211712 Adjacent sequences: A337228 A337229 A337230 * A337232 A337233 A337234 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Aug 20 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 24 09:00 EDT 2024. Contains 374575 sequences. (Running on oeis4.)