Intended for: August 7, 2011
Timetable
- First draft entered by Alonso del Arte on May 7, 2011 based on a write-up by Charles R. Greathouse. ✓
- Second draft to be entered by May 27, 2011 by which time A109794 will hopefully have been edited with a proof or disproof of its periodicity.
- Draft reviewed by Daniel Forgues on August 6, 2011 ✓, August 6, 2018 ✓
- Draft to be approved by July 7, 2011
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A109794:
A001906,
A002878. Equivalently,
[even index] bisection
A000045 of
Fibonacci numbers interleaved with
[odd index] bisection
A000204 of
Lucas numbers.
-
{ 1, 1, 3, 4, 8, 11, 21, 29, 55, 76, 144, 199, 377, 521, 987, 1364, 2584, 3571, 6765, 9349, 17711, 24476, ... }
This sequence, on the face of it, is just another linear recurrence relation (of order 4), e.g.
-
a (0) = 1, a (1) = 1, a (2) = 3, a (3) = 4; |
-
a (n) = 3 a (n − 2) − a (n − 4), n ≥ 4. |
It appears (proof?) that
A109794 A189761 where
A189761 gives numbers
for which the set of residues
{Fibonacci (k) mod n, k = 0, 1, 2, ...} |
is minimal, i.e.
A066853 A066853. It is also conjectured that the members of the sequence, for
, are just those
numbers for which the Pisano period is minimal: that is, conjecturally,
A001175 A001175 for all
iff
is in this sequence.