|
| |
|
|
A289586
|
|
Numbers k whose smallest multiple that is a Fibonacci number is Fibonacci(k).
|
|
1
|
|
|
|
1, 5, 12, 25, 60, 125, 300, 625, 1500, 3125, 7500, 15625, 37500, 78125, 187500, 390625, 937500, 1953125, 4687500, 9765625, 23437500, 48828125, 117187500, 244140625, 585937500, 1220703125, 2929687500, 6103515625, 14648437500, 30517578125, 73242187500, 152587890625, 366210937500
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Alternative names:
Numbers k such that Fibonacci(k) is the smallest positive Fibonacci number that is divisible by k.
Numbers that are their own Fibonacci entry points.
Numbers k such that k = A001177(k).
Numbers that are either a power of 5 or 12 times a power of 5. - Robert Israel, Aug 07 2017
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(2*k) = 5^k for k >= 1.
a(2*k-1) = 12*5^(k-2) for k >= 2.
G.f.: (1+5*x+7*x^2)/(1-5*x^2). (End)
|
|
|
EXAMPLE
|
Fibonacci(25) = 75025 = 25*3001 is the smallest Fibonacci number that is divisible by 25, so 25 is in the sequence.
Although Fibonacci(24) = 46368 = 24*1932 is divisible by 24, it is not the smallest Fibonacci number that is divisible by 24, so 24 is not in the sequence.
|
|
|
MAPLE
|
1, seq(op([5^k, 12*5^(k-1)]), k=1..100); # Robert Israel, Aug 07 2017
|
|
|
CROSSREFS
|
Subsequence of A023172 ("Self-Fibonacci numbers").
(Cf. A001602 for a different definition of "Fibonacci entry point".)
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
