1,15

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. Such values of n therefore require 0 steps to reduce. Many terms reduce in very few steps and others take longer (88 for example, takes 8 steps.) There is no maximum number of steps. See A090149 to see the first term requiring n steps. See A090147 to see the actual unchanging value reached for each value of n.

C. Seggelin, Interesting Base Conversions.

a(18)=4 because (1) 18 in base 9 is 17. (2) 17 in base 8 is 15. (3) 15 in base 6 is 11. (4) 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) 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) 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: A156906 A053094 A124516 this_sequence A071478 A071477 A071507

Adjacent sequences: A091045 A091046 A091047 this_sequence A091049 A091050 A091051

base,nonn

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