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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 Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-1). 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 Cf. A000045, A001906. Sequence in context: A014409 A303721 A109782 * A216893 A264245 A123044 Adjacent sequences: A237265 A237266 A237267 * A237269 A237270 A237271 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.)