A100993 -id:A100993 - cp's OEIS frontend

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

18, 108, 138, 198, 228, 348, 378, 618, 828, 858, 1278, 1428, 1488, 1608, 1668, 1698, 1788, 1878, 1998, 2028, 2088, 2238, 2268, 2658, 2688, 3168, 3258, 3468, 3528, 3558, 3768, 3918, 4128, 4158, 4218, 4338, 4518, 4548, 4638, 4788, 4968, 5418, 5478, 5658, 5778

Offset: 1

Michel Lagneau, May 02 2013

nonn

Intersection of A100992 and A100993.
Property of this sequence:
a(n) == 0 or 18 mod 30, but the case a(n) == 0 mod 30 is very rare (for n = 6480, 21000,... ).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000045, A100992, A100993.

[n: n in [2..10^4] | IsZero(Fibonacci(n) mod (n-1)) and IsZero(Fibonacci(n) mod (n+1))]; // Bruno Berselli, May 03 2013

Select[ Range[5800], Mod[ Fibonacci[ # ], # + 1]== 0 && Mod[ Fibonacci[ # ], # - 1] == 0 &]

is(n)=n%6==0 && ((Mod([1,1;1,0],n^2-1))^n)[1,2]==0 \\ Charles R Greathouse IV, May 02 2013

a(n) = {A100992(n)}intersection{A100993(n)}.

A100992 Indices k of Fibonacci numbers F(k) (A000045) that are divisible by k+1.

Original entry on oeis.org

10, 18, 28, 30, 40, 58, 60, 70, 78, 88, 100, 108, 130, 138, 148, 150, 178, 180, 190, 198, 210, 228, 238, 240, 250, 268, 270, 280, 310, 330, 348, 358, 378, 388, 400, 408, 418, 420, 430, 438, 441, 448, 460, 478, 490, 498, 508, 520, 540, 568, 570, 598, 600, 618

Offset: 1

Ron Knott, Nov 25 2004

nonn

When k+1 is prime, it is in A045468; when k+1 is composite (such as 442), it is in A069106. - T. D. Noe, Dec 13 2004

			18 is a term because F(18) = 2584 = 2*2*2*17*19 is divisible by 19, one more than its index number 18.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Ron Knott, Mathematical Magic of the Fibonacci Numbers.

Cf. A000045, A100993, A023162, A023173, A045468, A069106.

Select[ Range[ 620], Mod[ Fibonacci[ # ], # + 1] == 0 &] (* Robert G. Wilson v, Nov 26 2004 *)

More terms from Robert G. Wilson v, Nov 26 2004

cp's OEIS Frontend

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

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