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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

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

Subsequence of A023172 ("Self-Fibonacci numbers").

Cf. A000045, A001177, A000351 (bisection), A216491 (bisection)

(Cf. A001602 for a different definition of "Fibonacci entry point".)

Sequence in context: A086168 A301748 A108201 * A223233 A038254 A223321

Adjacent sequences:  A289583 A289584 A289585 * A289587 A289588 A289589

KEYWORD

nonn,easy

AUTHOR

Jon E. Schoenfield, Aug 06 2017

EXTENSIONS

More terms from Robert Israel, Aug 07 2017

STATUS

approved

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)