

A019446


a(n) = ceiling(n/tau), where tau = (1+sqrt(5))/2.


14



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
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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 n1=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
It seems that the indices of the terms that occur exactly once are listed in A276885.  Ivan N. Ianakiev, Aug 30 2018


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(n1)).  Benoit Cloitre, Nov 06 2002
a(n) = A005206(n) + 1.  Reinhard Zumkeller, Feb 02 2012
a(n) = A019445(n) / n.  Sean A. Irvine, Mar 17 2019


EXAMPLE

a(6)=4 since 61=[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 !! (n1)
a019446_list = 1 : zipWith () [3..] (map a019446 a019446_list)
 Reinhard Zumkeller, Feb 02 2012
(GAP) a:=[1];; for n in [2..80] do a[n]:=n+1a[a[n1]]; od; a; # Muniru A Asiru, Aug 30 2018


CROSSREFS

Cf. A001622, A019444, A019445, A026352, A005206.
Sequence in context: A256502 A177151 A076935 * A097369 A257808 A249036
Adjacent sequences: A019443 A019444 A019445 * A019447 A019448 A019449


KEYWORD

nonn,easy,nice,changed


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



