A273376 Pick any pair of "1" digits in the sequence. Those two "1"s are separated by k digits. This is the lexicographically earliest sequence of distinct terms in which all the resulting values of k are distinct.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 24, 25, 26, 27, 12, 28, 29, 13, 30, 32, 33, 14, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 15, 45, 46, 47, 48, 49, 50, 31, 52, 53, 54, 55, 41, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 51, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 61, 90, 92, 93, 94, 95, 96, 97, 98, 99, 200, 202, 203, 204, 205, 206, 201

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, May 30 2016

Keywords

• nonn
• base

Comments

The sequence starts with a(1)=0. It is then always extended with the smallest integer not yet present and not leading to a contradiction (which would mean producing a value of k already seen).

Examples

			The ten "k"s in the starting segment here are different [0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21,] and respectively equal to 8,10,11,15,1,2,6,0,4,3.
Indeed, there are k=8 digits between [1] and the "1" of [10] which are 2,3,4,5,6,7,8,9; there are k=10 digits between [1] and the first "1" of [11] which are 2,3,4,5,6,7,8,9,1,0;  there are k=11 digits between [1] and the second "1" of [11] which are 2,3,4,5,6,7,8,9,1,0,1; there are k=15 digits between [1] and the "1" of [21] which are 2,3,4,5,6,7,8,9,1,0,1,1,2,0,2.
There is k=1 digit between the "1" of [10] and the first "1" of [11] which is 0; there are k=2 digits between the "1" of [10] and the second "1" of [11] which are 0 and 1; there are k=6 digits between the "1" of [10] and the "1" of [21] which are 0,1,1,2,0,2.
There are k=0 digits between the first "1" of [11] and the second "1" of [11]; there are k=4 digits between the first "1" of [11] and the "1" of [21] which are 1,2,0,2.
There are k=3 digits between the second "1" of [11] and the "1" of [21] which are 2,0 and 2.
		

Links

• Eric Angelini, Table of n, a(n) for n = 1..1011