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A237268 a(1)=1; for n > 1, a(n) is the smallest F(m) > F(n) such that F(n) divides F(m), where F(k) denotes the k-th Fibonacci number. 2
1, 2, 8, 21, 55, 144, 377, 987, 2584, 6765, 17711, 46368, 121393, 317811, 832040, 2178309, 5702887, 14930352, 39088169, 102334155, 267914296, 701408733, 1836311903, 4807526976, 12586269025, 32951280099, 86267571272, 225851433717, 591286729879, 1548008755920 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) > Fibonacci(n) for n > 1.
{a(n)} = {F(2*n)} union {2} minus {0,3} where F(2*n) = A001906(n) = bisection of Fibonacci sequence.
LINKS
FORMULA
From Colin Barker, Jul 29 2014: (Start)
a(n) = 3*a(n-1) - a(n-2) for n>4.
G.f.: -x*(x^3 - 3*x^2 + x - 1) / (x^2 - 3*x + 1). (End)
a(n) = (((3 + sqrt(5))/2)^n - ((3 - sqrt(5))/2)^n)/sqrt(5) for n > 2. - Stefano Spezia, Apr 15 2022
EXAMPLE
377 is the first Fibonacci number that is divisible by 13, the 7th Fibonacci number, so a(7) = 377.
MAPLE
A237268 := proc(n)
coeftayl((1-x+3*x^2-x^3)/(x^2-3*x+1), x=0, n);
end proc:
seq(A237268(n), n=0..30); # Wesley Ivan Hurt, Aug 02 2014
MATHEMATICA
Table[k=1; While[Mod[Fibonacci[k], Fibonacci[n]]!=0||Fibonacci[k]==Fibonacci[n], k++]; Fibonacci[k], {n, 1, 30}]
CoefficientList[Series[-(x^3 - 3 x^2 + x - 1)/(x^2 - 3 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 01 2014 *)
PROG
(PARI) Vec(-x*(x^3-3*x^2+x-1)/(x^2-3*x+1) + O(x^100)) \\ Colin Barker, Jul 29 2014
CROSSREFS
Sequence in context: A014409 A303721 A109782 * A216893 A264245 A123044
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Feb 05 2014
STATUS
approved

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Last modified June 25 15:24 EDT 2024. Contains 373705 sequences. (Running on oeis4.)