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A298684 Numbers i such that Fibonacci(i) is divisible by i, i+1, and i+2.

%I A298684 #15 Sep 08 2022 08:46:20
%S A298684 60,540,660,1200,1320,1620,2160,3060,5580,6120,6600,6720,8100,9180,
%T A298684 9240,9600,9720,9900,11160,12240,12300,12600,13200,13440,13680,15120,
%U A298684 15360,18300,18480,19440,19800,21000,22500,24480,24840,26880,27360,28920,29400,30240,30780
%N A298684 Numbers i such that Fibonacci(i) is divisible by i, i+1, and i+2.
%C A298684 A subsequence of A217738.
%H A298684 Chai Wah Wu, <a href="/A298684/b298684.txt">Table of n, a(n) for n = 1..1000</a>
%t A298684 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 A298684 (Python)
%o A298684 from __future__ import division
%o A298684 A298684_list, n, a, b = [], 1, 1, 1
%o A298684 while len(A298684_list) < 1000:
%o A298684     if not (a % (n*(n+1)*(n+2)//(1 if n % 2 else 2))):
%o A298684         A298684_list.append(n)
%o A298684     n += 1
%o A298684     a, b = b, a+b # _Chai Wah Wu_, Jan 26 2018
%o A298684 (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 A298684 Cf. A000045, A023172, A217738, A221018, A225219.
%K A298684 nonn
%O A298684 1,1
%A A298684 _Alex Ratushnyak_, Jan 24 2018