login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 6
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 (list; graph; refs; listen; history; text; internal format)
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 { 1<=i<=k: Card[ contfrac(k/i) ] } a(1)=1 and 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)=3F(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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 11:35 EST 2018. Contains 317238 sequences. (Running on oeis4.)