Intended for: May 4, 2013
Timetable
- First draft entered by Alonso del Arte on March 22, 2012 ✓
- Draft reviewed by Daniel Forgues on May 03, 2016 ✓
- Draft to be approved by April 4, 2013
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A210209:
Greatest common divisor of all sums of
consecutive
Fibonacci numbers, for
.
-
{ 1, 1, 2, 1, 1, 4, 1, 3, 2, 11, 1, 8, ... }
If you add up any ten consecutive Fibonacci numbers, that sum is a multiple of
11. Or if you add up any fifty-nine consecutive Fibonacci numbers, that sum is a multiple of
1149851 (59 × 19489). For odd
, adding up
consecutive Fibonacci numbers gives either
coprime sums (
), or sums that have only
2 as a common factor (
) when
is divisible by
3. For even
, we get
if
is an even multiple of
2,
if
is an odd multiple of
2 (see
A005013).
