

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.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 5, 7, 9, 3, 7, 3, 3, 19, 6, 7, 8, 3, 9, 3, 6, 3, 6, 29, 5, 7, 9, 3, 19, 3, 3, 7, 3, 39, 6, 7, 8, 3, 9, 29, 19, 39, 9, 49, 5, 7, 9, 3, 19, 3, 7, 39, 3, 59, 8, 3, 9, 29, 19, 39, 9, 3, 9, 69, 7, 39, 3, 59, 8, 3, 9, 29, 39, 79, 3, 59, 8, 3, 9, 29, 39, 79, 3, 89, 90, 91, 92
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OFFSET

1,2


COMMENTS

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 singledigit number will likewise not reduce further. Many terms reduce in very few steps and others take longer (88 for example, takes 8 steps). See A091048 for the number of steps for each value of n. There is no maximum number of steps. See A091049 to see the first term requiring n steps.


LINKS

Table of n, a(n) for n=1..92.
C. Seggelin, Interesting Base Conversions.


EXAMPLE

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.


CROSSREFS

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: A322001 A081594 A038506 * A068505 A080719 A049105
Adjacent sequences: A091044 A091045 A091046 * A091048 A091049 A091050


KEYWORD

base,nonn


AUTHOR

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


STATUS

approved



