

A091048


a(n) = the number of steps needed to reach the final value of n via repeated interpretation of n as a base b+1 number where b is the largest digit of n.


3



0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 0, 1, 1, 1, 2, 2, 4, 2, 3, 3, 0, 2, 2, 2, 3, 1, 3, 4, 3, 4, 0, 2, 2, 2, 3, 3, 1, 2, 1, 4, 0, 3, 3, 3, 4, 2, 4, 3, 2, 5, 0, 3, 4, 4, 2, 3, 2, 5, 5, 5, 0, 4, 3, 6, 1, 4, 5, 5, 3, 4, 0, 7, 2, 5, 6, 6, 4, 5, 1, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
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OFFSET

1,15


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. 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 A091049 to see the first term requiring n steps. See A091047 to see the actual unchanging value reached for each value of n.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
C. Seggelin, Interesting Base Conversions.


EXAMPLE

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.


MAPLE

f:= proc(n) option remember;
local L, b, i;
if n < 10 then return 0 fi;
L:= convert(n, base, 10);
b:= max(L)+1;
if b = 10 then 0 else 1+procname(add(L[i]*b^(i1), i=1..nops(L))) fi
end proc:
map(f, [$1..100]); # Robert Israel, Feb 19 2018


CROSSREFS

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: A124516 A205958 A309090 * A071478 A071477 A071507
Adjacent sequences: A091045 A091046 A091047 * A091049 A091050 A091051


KEYWORD

base,nonn


AUTHOR

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


STATUS

approved



