A100992 -id:A100992 - 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)}.

A100993 Indices k of Fibonacci numbers F(k) (A000045) that are divisible by k-1.

Original entry on oeis.org

2, 3, 4, 8, 14, 18, 24, 38, 44, 48, 54, 68, 74, 84, 98, 104, 108, 114, 128, 138, 158, 164, 168, 174, 194, 198, 224, 228, 234, 258, 264, 278, 284, 294, 308, 314, 318, 324, 338, 348, 354, 368, 374, 378, 384, 398, 434, 444, 458, 464, 468, 488, 504, 524, 548, 558

Offset: 1

Ron Knott, Nov 25 2004

nonn

When k-1 is prime, it is in A003631; when k-1 is composite (such as 323), it is in A069107. - T. D. Noe, Dec 13 2004

			14 is a term because F(14) = 377 = 13*29 is divisible by 13, one less than its index number 14.

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

Cf. A000045, A100992, A003631, A023162, A023173, A069104, A069107.

Select[Range[2, 500], Mod[ Fibonacci[ # ], # - 1] == 0 &] (* Robert G. Wilson v, Nov 26 2004 *)

a(n) = A069104(n) + 1. - T. D. Noe, Dec 13 2004

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula