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

60, 540, 660, 1200, 1320, 1620, 2160, 3060, 5580, 6120, 6600, 6720, 8100, 9180, 9240, 9600, 9720, 9900, 11160, 12240, 12300, 12600, 13200, 13440, 13680, 15120, 15360, 18300, 18480, 19440, 19800, 21000, 22500, 24480, 24840, 26880, 27360, 28920, 29400, 30240, 30780

Offset: 1

Author

Alex Ratushnyak, Jan 24 2018

Keywords

• nonn

Comments

A subsequence of A217738.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A023172, A217738, A221018, A225219.

Programs

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

Mathematica

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 *)

Python

from _future_ import division
A298684_list, n, a, b = [], 1, 1, 1
while len(A298684_list) < 1000:
    if not (a % (n*(n+1)*(n+2)//(1 if n % 2 else 2))):
        A298684_list.append(n)
    n += 1
    a, b = b, a+b # Chai Wah Wu, Jan 26 2018