A023175 Numbers k such that Fibonacci(k) == 3 (mod k).

1, 2, 4, 76, 124, 196, 244, 316, 374, 436, 556, 604, 724, 796, 844, 916, 964, 1084, 1324, 1396, 1516, 1636, 1684, 1756, 1768, 1804, 1996, 2164, 2284, 2404, 2476, 2524, 2644, 2764, 2836, 2956, 3004, 3076, 3244, 3316, 3436, 3676, 3964, 4036, 4084, 4156, 4204

Offset

1,2

Comments

Among the first 10000 terms, all are even except for 1 and 20017. - Robert Israel, Sep 22 2023

Contains k if k == 4 (mod A001175(k)). In particular, this is the case if k = 4 * p where p is a prime == 1 or 19 (mod 30). Most terms appear to be of this type, including all but 141 of the first 10000 terms. - Robert Israel, Sep 24 2023

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n) uses LinearAlgebra:-Modular; local A;
  A:= Mod(n, Matrix([[0, 1], [1, 1]]), integer[]);
  MatrixPower(n, A, n)[1, 2] - 3 mod n = 0
end proc:
filter(1):= true:
select(filte, [$1..10000]); # Robert Israel, Sep 22 2023

Mathematica

Select[Table[{p, Fibonacci[p]}, {p, 4500}], Mod[Last[#]-3, First[#]]==0&][[All, 1]] (* Harvey P. Dale, Sep 22 2021 *)

Crossrefs

Cf. A000045, A001175.

Sequence in context: A292414 A053550 A018378 * A276740 A006688 A292711

Adjacent sequences: A023172 A023173 A023174 * A023176 A023177 A023178

Keyword

nonn

Author

David W. Wilson

Status

approved