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%I #24 Jan 09 2024 16:12:33
%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-François Alcover_, Sep 12 2017 *)
%K nonn,look
%O 1,2
%A _Clark Kimberling_