A069104 Numbers m such that m divides Fibonacci(m+1).

1, 2, 3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 127, 137, 157, 163, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 313, 317, 323, 337, 347, 353, 367, 373, 377, 383, 397, 433, 443, 457, 463, 467, 487, 503, 523, 547, 557

Offset: 1

Author

Benoit Cloitre, Apr 06 2002

Keywords

• easy
• nonn

Comments

Equals A003631 union A069107.

Let u(1)=u(2)=1 and (m+2)*u(m+2) = (m+1)*u(m+1) + m*u(m); then sequence gives values of k such that u(k) is an integer.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A023172, A123976, A159051.

Programs

Haskell

import Data.List (elemIndices)
a069104 n = a069104_list !! (n-1)
a069104_list =
   map (+ 1) $ elemIndices 0 $ zipWith mod (drop 2 a000045_list) [1..]
-- Reinhard Zumkeller, Oct 13 2011

Mathematica

Select[Range[6! ],IntegerQ[Fibonacci[ #+1]/# ]&] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Select[Range[600],Mod[Fibonacci[#+1],#]==0&] (* Harvey P. Dale, Feb 24 2025 *)

PARI

is(n)=((Mod([1,1;1,0],n))^n)[1,1]==0 \\ Charles R Greathouse IV, Feb 03 2014