|
Search: id:A072378
|
|
|
| A072378 |
|
Numbers n such that 12n divides F(12n) where F(m) is the m-th Fibonacci number. |
|
+0
5
|
|
| 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 25, 27, 28, 30, 32, 36, 40, 42, 45, 46, 48, 50, 51, 54, 55, 56, 57, 60, 64, 70, 72, 75, 80, 81, 84, 90, 92, 96, 98, 100, 102, 108, 110, 112, 114, 120, 125, 126, 128, 135, 138, 140, 144, 150, 153, 155, 160, 162, 165
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The numbers n such that n divides the n-th Fibonacci number seem to consist of the powers of 5 and some multiples of 12. (We can prove that the powers of 5 have this property and that if n is even and has this property then n is a multiple of 12.) The n-th number in the sequence seems to be asymptotic to a constant multiple of n^phi where phi is the golden ratio.
|
|
EXAMPLE
|
3 belongs to the sequence because 3*12=36 divides F(36)=14930352. For every n, 5^n belongs to the sequence, as can be proved by induction.
|
|
MATHEMATICA
|
Select[Range[n], Mod[Fibonacci[12# ], 12# ]==0&]
|
|
CROSSREFS
|
Sequence in context: A064390 A080671 A124455 this_sequence A112587 A068090 A094222
Adjacent sequences: A072375 A072376 A072377 this_sequence A072379 A072380 A072381
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Omar Antolin Camarena (omar(AT)tlahui.posgrado.unam.mx), Jul 19 2002
|
|
|
Search completed in 0.002 seconds
|
