A335925 a(n) = a(floor((n-1)/a(n-1))) + 1 with a(1) = 1.

1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 4, 5, 4

Offset: 1

Author

Altug Alkan, Jun 30 2020

Keywords

• nonn
• easy

Comments

Least k such that a(k) = n are 1, 2, 5, 16, 65, 326, 1957, ... (Conjecture: This sequence is A000522).

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A130147, A288914, A335901.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = a[Floor[(n - 1)/a[n - 1]]] + 1 ; Array[a, 100] (* Amiram Eldar, Jun 30 2020 *)

PARI

a=vector(10^2); a[1]=1; for(n=2, #a, a[n]=a[(n-1)\a[n-1]]+1); a;