A071679 Least k such that the maximum number of elements among the continued fractions for k/1, k/2, k/3, k/4, ..., k/k equals n.

1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..4784

Mohammad K. Azarian, Fibonacci Identities as Binomial Sums, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 38, 2012, pp. 1871-1876 (See Corollary 1 (x)).

Index entries for linear recurrences with constant coefficients, signature (1,1).

Formula

Smallest k such that n = Max_{ i=1..k: Card[ contfrac(k/i) ] }.

a(1) = 1; for n>1 a(n) = F(n+2) where F(n)=A000045(n) are the Fibonacci numbers.

G.f.: (1+x)^2/(1-x-x^2); a(n) = 3*F(n+1) - F(n-1) - 0^n. - Paul Barry, Jul 26 2004

a(n) = Fibonacci(n+2) for n > 1. - Charles R Greathouse IV, Jan 17 2012

Mathematica

Join[{1}, LinearRecurrence[{1, 1}, {3, 5}, 50]] (* Vincenzo Librandi, Jul 12 2015 *)

Prog

(PARI) a(n)=if(n>1, fibonacci(n+2), 1) \\ Charles R Greathouse IV, Jan 17 2012
(Magma) [1] cat [Fibonacci(n+2): n in [2..50]]; // Vincenzo Librandi, Jul 12 2015

Crossrefs

Cf. A000045, A324969.

Sequence in context: A079122 A265069 A265070 * A020701 A024885 A180459

Adjacent sequences: A071676 A071677 A071678 * A071680 A071681 A071682

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 22 2002

Status

approved