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

1,2

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)

Links

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

Example

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.

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 *)

Crossrefs

Cf. A002283, A011540, A284062-A284069.

Sequence in context: A297353 A172503 A107859 * A249585 A067524 A069555

Adjacent sequences: A294066 A294067 A294068 * A294070 A294071 A294072

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Feb 07 2018

Status

approved