1,2

Any value of n with at least one digit 9 will not reduce further since 9+1 is 10 and n in base 10 is n. Also any single digit number will likewise not reduce further. Many terms reduce in very few steps and others take longer (88 for example, takes 8 steps.) See A090148 for the number of steps for each value of n. There is no maximum number of steps. See A090149 to see the first term requiring n steps.

C. Seggelin, Interesting Base Conversions.

a(18)=3 because 18 in base 9 is 17. 17 in base 8 is 15. 15 in base 6 is 11. 11 in base 2 is 3. 3 does not reduce further because 3 in base 4 is 3. Thus 18 reduces to 3 in 4 steps.

Cf. A054055 (largest digit of n) A068505 (n as base b+1 number where b=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) A091049 (a(n) = first term which reduces to an unchanging value in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n)).

Sequence in context: A028897 A081594 A038506 this_sequence A068505 A080719 A049105

Adjacent sequences: A091044 A091045 A091046 this_sequence A091048 A091049 A091050

base,nonn

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