A123976 - OEIS

%I #12 Feb 03 2014 22:57:24

%S 1,11,19,29,31,41,59,61,71,79,89,101,109,131,139,149,151,179,181,191,

%T 199,211,229,239,241,251,269,271,281,311,331,349,359,379,389,401,409,

%U 419,421,431,439,442,449,461,479,491,499,509,521,541,569,571,599,601

%N Numbers n such that Fibonacci(n-1) is divisible by n.

%C 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

%H Reinhard Zumkeller, <a href="/A123976/b123976.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%o (Haskell)

%o import Data.List (elemIndices)

%o a123976 n = a123976_list !! (n-1)

%o a123976_list = map (+ 1) $ elemIndices 0 $ zipWith mod a000045_list [1..]

%o -- _Reinhard Zumkeller_, Oct 13 2011

%o (PARI) is(n)=((Mod([1,1;1,0],n))^n)[2,2]==0 \\ _Charles R Greathouse IV_, Feb 03 2014

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

%K nonn

%O 1,2

%A _Tanya Khovanova_, Oct 30 2006