A133418 Let l(n) = number of letters in n, A005589(n). If l(n) = 4 set a(n) = 0; otherwise a(n) = a(l(n)) + 1.

0, 2, 2, 1, 0, 0, 2, 1, 1, 0, 2, 3, 3, 2, 2, 2, 2, 1, 2, 2, 3, 1, 1, 4, 3, 3, 1, 4, 4, 3, 3, 1, 1, 4, 3, 3, 1, 4, 4, 3, 1, 2, 2, 3, 1, 1, 2, 3, 3, 1, 1, 2, 2, 3, 1, 1, 2, 3, 3, 1, 1, 2, 2, 3, 1, 1, 2, 3, 3, 1, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 3, 1, 1, 4, 3, 3, 1, 4, 4, 3, 3, 1, 1, 4, 3, 3, 1, 4, 4, 3, 4, 3, 3, 3, 3

Offset: 0

Author

N. J. A. Sloane, Nov 27 2007

Keywords

• nonn
• word
• easy

Comments

Based on the observation by Diane Karloff (see A005589) that the trajectory of l always converges to 4.

The smallest n with a(n) = 6 is 1103323373373373373373373373373 (one nonillion one hundred and three octillion ...) which has 323 letters.

Examples

			5 has four letters so a(5) = 0. 3 has five letters so a(3) = a(5) + 1 = 1.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 0..11999
• R. J. Mathar, Maple program to make b-file

Crossrefs

A variant of A016037.