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 A019446 a(n) = ceiling(n/tau), where tau = (1+sqrt(5))/2. 15
 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 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(n-1)). - 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 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/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 (GAP) a:=;; for n in [2..80] do a[n]:=n+1-a[a[n-1]]; 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 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

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Last modified September 21 04:59 EDT 2019. Contains 327253 sequences. (Running on oeis4.)