login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A298684
Numbers i such that Fibonacci(i) is divisible by i, i+1, and i+2.
8
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
1,1
COMMENTS
A subsequence of A217738.
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 *)
PROG
(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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Jan 24 2018
STATUS
approved