%I #15 Sep 08 2022 08:46:20

%S 60,540,660,1200,1320,1620,2160,3060,5580,6120,6600,6720,8100,9180,

%T 9240,9600,9720,9900,11160,12240,12300,12600,13200,13440,13680,15120,

%U 15360,18300,18480,19440,19800,21000,22500,24480,24840,26880,27360,28920,29400,30240,30780

%N Numbers i such that Fibonacci(i) is divisible by i, i+1, and i+2.

%C A subsequence of A217738.

%H Chai Wah Wu, <a href="/A298684/b298684.txt">Table of n, a(n) for n = 1..1000</a>

%t fQ[n_] := Mod[ Fibonacci@ n, {n, n +1, n +2}] == {0, 0, 0}; Select[60 Range@513, fQ] (* _Robert G. Wilson v_, Jan 26 2018 *)

%o (Python)

%o from __future__ import division

%o A298684_list, n, a, b = [], 1, 1, 1

%o while len(A298684_list) < 1000:

%o if not (a % (n*(n+1)*(n+2)//(1 if n % 2 else 2))):

%o A298684_list.append(n)

%o n += 1

%o a, b = b, a+b # _Chai Wah Wu_, Jan 26 2018

%o (Magma) [n: n in [2..10^5] | IsZero(Fibonacci(n) mod (n)) and IsZero(Fibonacci(n) mod (n+1)) and IsZero(Fibonacci(n) mod (n+2))]; // _Vincenzo Librandi_, Jan 27 2018

%Y Cf. A000045, A023172, A217738, A221018, A225219.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Jan 24 2018