A123976 Numbers k such that Fibonacci(k-1) is divisible by k.

1, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 442, 449, 461, 479, 491, 499, 509, 521, 541, 569, 571, 599, 601

Offset: 1

Author

Tanya Khovanova, Oct 30 2006

Keywords

• nonn

Comments

a(n) is a union of {1}, A069106(n) and A045468(n). Composite a(n) are listed in A069106(n) = {442, 1891, 2737, 4181, 6601, 6721, 8149, ...}. Prime a(n) are listed in A045468(n) = {11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, ...} Primes congruent to {1, 4} mod 5. - Alexander Adamchuk, Nov 02 2006

Examples

			Fibonacci(10) = 55, is divisible by 11.
		

Links

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

Crossrefs

Cf. A069106, A045468, A069104, A069107, A003631, A000045, A023172, A159051.

Programs

Haskell

import Data.List (elemIndices)
a123976 n = a123976_list !! (n-1)
a123976_list = map (+ 1) $ elemIndices 0 $ zipWith mod a000045_list [1..]
-- Reinhard Zumkeller, Oct 13 2011

Mathematica

Select[Range[1000], IntegerQ[Fibonacci[ # - 1]/# ] &]

PARI

is(n)=((Mod([1,1;1,0],n))^n)[2,2]==0 \\ Charles R Greathouse IV, Feb 03 2014