A095205 Least nonnegative integer not already in the sequence such that the frequency of digits in the entire sequence is as close to a uniform distribution as possible. A difference in frequency of at most 1 across all digits is allowed, and that difference must always be in favor of digits closer to 0.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 45, 67, 89, 102, 34, 56, 78, 90, 12, 43, 65, 87, 109, 32, 54, 76, 98, 120, 345, 678, 190, 234, 567, 809, 21, 354, 687, 901, 243, 576, 890, 123, 456, 789, 201, 435, 768, 910, 324, 657, 908, 132, 465, 798, 210, 453, 786, 1029

Offset: 0

Author

Amarnath Murthy, Jun 06 2004

Keywords

• base
• nonn

Comments

Obviously no term contains identical digits and eventually for some m, a(m) = 1023456789 = a(n) for all n > m. Let d = number of numbers containing all distinct digits, using digits 0 to 9, then is it conjectured that: m is not equal to d, i.e., m < d. Question: what is m?

Examples

			After 89 the next term is 102. It is not 11 or 12 as 0 has to occur first, it is not 20 as 1 has to occur earlier to 2.
		

Links

• Micah Manary, Table of n, a(n) for n = 0..1000
• Micah Manary, Python script for A095205

Crossrefs

Cf. A095204.

Extensions

Better definition and more terms from Micah Manary, Nov 13 2019