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A225219 Indices n of Fibonacci numbers Fib(n) (A000045) that are divisible by n-1 and n+1.

%I A225219 #12 Sep 08 2022 08:46:04
%S A225219 18,108,138,198,228,348,378,618,828,858,1278,1428,1488,1608,1668,1698,
%T A225219 1788,1878,1998,2028,2088,2238,2268,2658,2688,3168,3258,3468,3528,
%U A225219 3558,3768,3918,4128,4158,4218,4338,4518,4548,4638,4788,4968,5418,5478,5658,5778
%N A225219 Indices n of Fibonacci numbers Fib(n) (A000045) that are divisible by n-1 and n+1.
%C A225219 Intersection of A100992 and A100993.
%C A225219 Property of this sequence:
%C A225219 a(n) == 0 or 18 mod 30, but the case a(n) == 0 mod 30 is very rare (for n = 6480, 21000,... ).
%H A225219 Charles R Greathouse IV, <a href="/A225219/b225219.txt">Table of n, a(n) for n = 1..10000</a>
%F A225219 a(n) = {A100992(n)}intersection{A100993(n)}.
%t A225219 Select[ Range[5800], Mod[ Fibonacci[ # ], # + 1]== 0 && Mod[ Fibonacci[ # ], # - 1] == 0 &]
%o A225219 (PARI) is(n)=n%6==0 && ((Mod([1,1;1,0],n^2-1))^n)[1,2]==0 \\ _Charles R Greathouse IV_, May 02 2013
%o A225219 (Magma) [n: n in [2..10^4] | IsZero(Fibonacci(n) mod (n-1)) and IsZero(Fibonacci(n) mod (n+1))]; // _Bruno Berselli_, May 03 2013
%Y A225219 Cf. A000045, A100992, A100993.
%K A225219 nonn
%O A225219 1,1
%A A225219 _Michel Lagneau_, May 02 2013