A225219 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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,... ).

LINKS

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

FORMULA

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

MATHEMATICA

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

PROG

(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

(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

CROSSREFS

Cf. A000045, A100992, A100993.

Sequence in context: A123277 A123595 A317461 * A002165 A008654 A060787

Adjacent sequences: A225216 A225217 A225218 * A225220 A225221 A225222

KEYWORD

nonn

AUTHOR

Michel Lagneau, May 02 2013

STATUS

approved