OFFSET
1,2
COMMENTS
The sequence is bounded. Let us consider a k-digit number n in which all 10 numerals from 0 to 9 are equally distributed: there are k/10 0's, k/10 1's, etc. This is the best case in order to have a number with the greatest number of digits under the transform n -> A047842(n). The number of digits we get is 10 + 10*floor(log_10(k/10) + 1), which must be >= k. The inequality becomes log_10(k/10) >= k/10 - 2, which is solved by k <= 23.75... This means that no term of the sequence can have more than 23 digits.
LINKS
EXAMPLE
A237605(258) = 121518 and 121518/258 = 471.
MAPLE
with(numtheory): P:=proc(q) local a, b, c, d, j, k, n; for n from 1 to q do
a:=sort(convert(n, base, 10)); k:=1; b:=a[1]; c:=0; for j from 2 to nops(a) do
if a[j]=b then k:=k+1; else d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; k:=1; b:=a[j]; fi; od;
d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; if type(c/n, integer) then print(n); fi; od; end: P(10^10);
CROSSREFS
KEYWORD
nonn,base,easy,fini
AUTHOR
Paolo P. Lava, Nov 22 2016
STATUS
approved