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)).

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, 30, 67, 29, 12, 26, 58, 25, 55, 122, 54, 120, 53, 23, 51, 114, 50, 111, 49, 21, 46, 102, 45, 100, 223, 99, 221, 98, 43, 96, 214, 95, 212, 94, 210

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• look

Comments

Does every positive integer occur exactly once?

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

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Programs

Mathematica

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 *)