A294069 The smallest digit of a(n+1) is strictly smaller than the largest digit of a(n).

1, 10, 20, 11, 30, 2, 12, 13, 14, 3, 15, 4, 16, 5, 17, 6, 18, 7, 19, 8, 21, 31, 22, 40, 23, 24, 25, 26, 27, 28, 29, 32, 41, 33, 42, 34, 35, 36, 37, 38, 39, 43, 50, 44, 51, 45, 46, 47, 48, 49, 52, 53, 54, 60, 55, 61, 56, 57, 58, 59, 62, 63, 64, 65, 70, 66

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Feb 07 2018

Keywords

• base
• nonn

Comments

The sequence starts with a(1) = 1 and was always extended with the smallest integer not yet present and not leading to a contradiction.

From Robert G. Wilson v, Feb 07 2018: (Start)

Inverse: 1, 6, 10, 12, 14, 16, 18, 20, 2, 4, 7, 8, 9, 11, 13, 15, 17, 19, 3, ..., .

Permutation of the Integers.

(End)

Examples

			The "0" of 10 is strictly < "1", which is the largest digit of 1;
The "0" of 20 is strictly < "1", which is the largest digit of 10;
The "1" of 11 is strictly < "2", which is the largest digit of 20;
The "0" of 30 is strictly < "1", which is the largest digit of 11;
The "2" of 2 is strictly < "3", which is the largest digit of 30;
The "1" of 12 is strictly < "2", which is the largest digit of 2; etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A002283, A011540, A284062-A284069.

Programs

Mathematica

f[s_List] := Block[{k = 1, mx = Max@IntegerDigits@s[[-1]]}, While[MemberQ[s, k] || Min@IntegerDigits@k >= mx, k++]; Append[s, k]]; Nest[f, {1}, 80] (* Robert G. Wilson v, Feb 07 2018 *)