A095204 a(n) is the smallest number greater than a(n-1) such that in a(0) through a(n) no digit occurs more than once more than any other digit.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 45, 67, 89, 90, 123, 456, 478, 501, 623, 789, 790, 812, 3456, 3457, 6012, 6089, 7123, 8459, 8460, 9123, 9157, 20345, 20678, 31456, 31789, 40256, 40789, 51236, 51789, 60234, 60789, 71234, 71589, 80234, 80569, 91234, 91567

Offset: 0

Author

Amarnath Murthy, Jun 06 2004

Keywords

• base
• nonn

Comments

Question: Formula for a(n)?

Note that, almost always, if the number of digits in a(0) through a(n) is a multiple of 10, a(n+1) = a(n) + 1. (The only exceptions would be if a(n) + 1 had some digit two more times than some other digit.) - Franklin T. Adams-Watters, Jan 11 2006

Examples

			After 10 the next term is 23 and not 11. Any number containing 0 or 1 would occur only after all the digits from 2 to 9 have occurred once.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..91

Crossrefs

Cf. A120125 (non-monotonic version).

Programs

Maple

counts:= Array(0..9):
cp:= Array(0..9):
counts[0]:= 1:
A[0]:= 0:
for n from 1 to 70 do
  for x from A[n-1]+1 do
     L:= convert(x,base,10);
     ArrayTools:-Copy(counts,cp);
     for t in L do cp[t]:= cp[t]+1 od:
     if max(cp) - min(cp) <= 1 then
        A[n]:= x;
        ArrayTools:-Copy(cp,counts);
        break
     fi
  od
od:
seq(A[i],i=0..70); # Robert Israel, Sep 03 2015

Extensions

Edited, corrected and extended by Franklin T. Adams-Watters, Jan 11 2006