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

0,3

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

Links

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

Example

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.

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

Crossrefs

Cf. A120125 (non-monotonic version).

Sequence in context: A120125 A345227 A333832 * A106604 A095205 A344325

Adjacent sequences: A095201 A095202 A095203 * A095205 A095206 A095207

Keyword

base,nonn

Author

Amarnath Murthy, Jun 06 2004

Extensions

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

Status

approved