This site is supported by donations to The OEIS Foundation.

Template:Sequence of the Day for May 4

From OeisWiki
Jump to: navigation, search

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
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A210209: Greatest common divisor of all sums of
n
consecutive Fibonacci numbers, for
n   ≥   1
.
{ 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
n
, adding up
n
consecutive Fibonacci numbers gives either coprime sums (
GCD = 1
), or sums that have only 2 as a common factor (
GCD = 2
) when
n
is divisible by 3. For even
n
, we get
Fn / 2
if
n
is an even multiple of 2,
Ln / 2
if
n
is an odd multiple of 2 (see A005013).