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

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A019446 a(n) = ceiling(n/tau), where tau=(1+sqrt(5))/2. 13
1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 18, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 44, 45, 46, 46 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Average of first n terms of A019444, which is defined to be a permutation of the positive integers, p_1, p_2, ..., such that the average of each initial segment is an integer, using the greedy algorithm to define p_n.

Number of pairs (i,j) of nonnegative integers such that n-1=floor(i+j*tau). - Clark Kimberling, Jun 18 2002

The terms that occur exactly once are 1,3,6,8,..., given by A026352(n)=n+1+floor(n*tau). - Clark Kimberling, Jun 18 2002

The number n appears A001468(n) times. - Reinhard Zumkeller, Feb 02 2012

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Problem of the week, Problem 818

J. Rickard, Rearrangement of the natural numbers

FORMULA

a(1)=1; a(n) = n+1 - a(a(n-1)). - Benoit Cloitre, Nov 06 2002

a(n) = A005206(n) + 1. - Reinhard Zumkeller, Feb 02 2012

EXAMPLE

a(6)=4 since 6-1=[i+j*tau] for these (i,j): (5,0), (4,1), (2,2), (1,3). - Clark Kimberling, Jun 18 2002

MAPLE

A019446:=n->ceil(2*n/(1+sqrt(5))); seq(A019446(n), 1..100); # Wesley Ivan Hurt, Jan 19 2014

MATHEMATICA

Ceiling[Range[80]/GoldenRatio] (* Harvey P. Dale, Aug 02 2011 *)

PROG

(Haskell)

a019446 n = a019446_list !! (n-1)

a019446_list = 1 : zipWith (-) [3..] (map a019446 a019446_list)

-- Reinhard Zumkeller, Feb 02 2012

CROSSREFS

Cf. A019444, A019445, A026352, A005206.

Sequence in context: A210434 A256502 A076935 * A097369 A257808 A249036

Adjacent sequences:  A019443 A019444 A019445 * A019447 A019448 A019449

KEYWORD

nonn,easy,nice

AUTHOR

R. K. Guy, Tom Halverson (halverson(AT)macalester.edu)

EXTENSIONS

Better name from David Radcliffe and John Rickard, Dec 12 2000

Edited by Dean Hickerson, Nov 09 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 August 18 18:11 EDT 2017. Contains 290732 sequences.