A103618 Number of steps required for n to reach a digit count invariant or cycle loop under the 'Look and Say' function A045918.
10, 12, 11, 12, 8, 10, 10, 10, 10, 10, 9, 11, 10, 11, 7, 9, 9, 9, 9, 9, 6, 10, 0, 9, 6, 6, 6, 6, 6, 6, 8, 11, 9, 10, 6, 8, 8, 8, 8, 8, 9, 7, 6, 6, 7, 8, 9, 9, 9, 9, 10, 9, 6, 8, 8, 7, 9, 10, 10, 10, 12, 9, 6, 8, 9, 9, 7, 10, 12, 12, 13, 9, 6, 8, 9, 10, 10, 7, 12, 13, 14, 9, 6, 8, 9, 10, 12, 12, 7, 13
Offset: 1
Examples
a(10)=9 because we have the 9-step chain 10 -> 1011 -> 1031 -> 102113 -> 103112113 -> 10411223 -> 1031221314 -> 1041222314 -> 1031321324 -> 1031223314, the latter being autobiographical, hence invariant. Also, a(40)=9 since we have the digit count iteration 40 -> 1014 -> 102114 -> 10311214 -> 1041121314 -> 1051121324 -> 104122131415 -> 105122132415 -> 104132131425 -> 104122232415 <-> 103142132415, ending in a 2-cycle loop.
Links
- Madras Math., Descriptive Numbers: Table of results
Extensions
Corrected and extended by Sean A. Irvine, Feb 08 2010