0,2

There is no maximum number of steps and for any value of n, there MUST be a term a(n) that reduces in n steps. This is demonstrable as follows: take any term in the above sequence and convert it to base 2. The resulting value, if interpreted as a base 10 value will require one additional step to reduce. The resulting value may not be the FIRST value to resolve in that many steps, however, so it may not belong in this sequence.

C. Seggelin, Interesting Base Conversions.

a(0) = 1 because 1 is the first term that reduces to an unchanging value in zero steps (i.e. 1 is already fully reduced.) a(1) = 10 because 10 reduces in one step (10 in base 2 is 2, 2 does not reduce further.) a(8) = 88 because 88 reduces in 8 steps: 88 --> 80 --> 72 --> 58 --> 53 --> 33 --> 15 --> 11 --> 3.

Cf. A054055 (largest digit of n) A068505 (n as base b+1 number where b=largest digit of n) A091047 (a(n) = the final value of n reached through repeated interpretation of n as a base b+1 number where b is the largest digit of n) A091048 (number of times n must be interpreted as a base b+1 number where b is the largest digit of n until an unchanging value is reached).

Sequence in context: A046424 A076226 A122435 this_sequence A139540 A135363 A118717

Adjacent sequences: A091046 A091047 A091048 this_sequence A091050 A091051 A091052

base,more,nonn

Chuck Seggelin (barkeep(AT)plastereddragon.com), Dec 15 2003, Jul 09 2008