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A050170 a(1) = 1, a(n) = floor(a(n-1)/sqrt(5)) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = floor(a(n-1))*sqrt(5)). 5

%I

%S 1,2,4,8,3,6,13,5,11,24,10,22,9,20,44,19,42,18,40,17,7,15,33,14,31,69,

%T 30,67,29,12,26,58,25,55,122,54,120,53,23,51,114,50,111,49,21,46,102,

%U 45,100,223,99,221,98,43,96,214,95,212,94,210

%N a(1) = 1, a(n) = floor(a(n-1)/sqrt(5)) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = floor(a(n-1))*sqrt(5)).

%C Does every positive integer occur exactly once?

%C Records occur at indices 1, 2, 3, 4, 7, 10, 15, 26, 35, 50, 87, 124, 179, 306, ... with corresponding values 1, 2, 4, 8, 13, 24, 44, 69, 122, 223, 348, 614, 1118, 1744, .... - _Peter Kagey_, Jan 24 2018

%H Ivan Neretin, <a href="/A050170/b050170.txt">Table of n, a(n) for n = 1..10000</a>

%t a[1] = 1; a[n_] := a[n] = If[FreeQ[Join[{0}, Array[a, n-1]], f = Floor[a[n-1]/Sqrt[5]]], f, Floor[a[n-1]*Sqrt[5]]]; Array[a, 60] (* _Jean-Fran├žois Alcover_, Sep 12 2017 *)

%K nonn,look

%O 1,2

%A _Clark Kimberling_

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Last modified September 19 12:50 EDT 2021. Contains 347556 sequences. (Running on oeis4.)