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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335673 Composite integers m such that A003500(m) == 4 (mod m). 4
10, 209, 230, 231, 399, 430, 455, 530, 901, 903, 923, 989, 1295, 1729, 1855, 2015, 2211, 2345, 2639, 2701, 2795, 2911, 3007, 3201, 3439, 3535, 3801, 4823, 5291, 5719, 6061, 6767, 6989, 7421, 8569, 9503, 9591, 9869, 9890, 10439, 10609, 11041, 11395, 11951, 11991 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If p is a prime, then A003500(p)==4 (mod p).
This sequence contains the composite integers for which the congruence holds.
The generalized Pell-Lucas sequences of integer parameters (a,b) defined by V(n+2)=a*V(n+1)-b*V(n) 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=4, b=1, V(n)=A003500(n).
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..10000 (first 1000 odd terms from Chai Wah Wu)
D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).
EXAMPLE
m=10 is the first composite integer for which A003500(m)==4 (mod m).
MATHEMATICA
Select[Range[3, 20000], CompositeQ[#] && Divisible[Round@LucasL[2#, Sqrt[2]] - 4, #] &] (* Amiram Eldar, Jun 18 2020 *)
PROG
(PARI) my(M=[1, 2; 1, 3]); forcomposite(m=5, 10^5, if(trace(Mod(M, m)^m)==4, print1(m, ", "))); \\ Joerg Arndt, Jun 18 2020
CROSSREFS
Cf. A005248, A335669 (a=3,b=-1), A335672 (a=3,b=1), A335674 (a=5,b=1).
A330206 is the subsequence of odd terms.
Sequence in context: A245918 A368441 A211107 * A215555 A069863 A160476
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Jun 17 2020
EXTENSIONS
More terms from Joerg Arndt, Jun 18 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)