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
Robert Israel, Table of n, a(n) for n = 1..2858
Index entries for linear recurrences with constant coefficients, signature (0,5).
FORMULA
From Robert Israel, Aug 07 2017: (Start)
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
KEYWORD
nonn,easy
AUTHOR
Jon E. Schoenfield, Aug 06 2017
EXTENSIONS
More terms from Robert Israel, Aug 07 2017
STATUS
approved