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A019446
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a(n) = ceiling(n/tau), where tau=(1+sqrt(5))/2.
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12
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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; internal format)
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OFFSET
| 1,2
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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 (ck6(AT)evansville.edu), 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 (ck6(AT)evansville.edu), Jun 18 2002
The number n appears A001468(n) times. [Reinhard Zumkeller, Feb 02 2012]
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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
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FORMULA
| a(1)=1; a(n) = n+1 - a(a(n-1)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 06 2002
a(n) = A005206(n) + 1. [Reinhard Zumkeller, Feb 02 2012]
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EXAMPLE
| a(6)=4 since 6-1=[i+j*tau] for these (i,j): (5,0), (4,1), (2,2), (1,3). - Clark Kimberling (ck6(AT)evansville.edu), Jun 18 2002
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MATHEMATICA
| Ceiling[Range[80]/GoldenRatio] (* From Harvey P. Dale, Aug 02 2011 *)
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PROG
| (Haskell)
a019446 n = a019446_list !! (n-1)
a019446_list = 1 : zipWith (-) [3..] (map a019446 a019446_list)
-- Reinhard Zumkeller, Feb 02 2012
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CROSSREFS
| Cf. A019444, A019445, A026352, A005206.
Sequence in context: A074840 A064542 A076935 * A097369 A096607 A103416
Adjacent sequences: A019443 A019444 A019445 * A019447 A019448 A019449
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| R. K. Guy, Tom Halverson (halverson(AT)macalester.edu)
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EXTENSIONS
| Better name from David Radcliffe (dradcliffe(AT)gmail.com) and John Rickard, Dec 12 2000
Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Nov 09 2002
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