A303166 Lexicographically earliest sequence of distinct terms such that the successive quantities of digits between two successive 7's are given by the succession of the sequence's digits itself.

0, 1, 2, 3, 4, 5, 6, 7, 70, 71, 8, 72, 9, 17, 10, 11, 73, 12, 13, 74, 14, 15, 27, 16, 18, 19, 37, 20, 21, 22, 47, 75, 23, 24, 25, 76, 78, 26, 28, 29, 57, 30, 31, 32, 67, 33, 79, 34, 35, 36, 38, 707, 39, 40, 41, 87, 97, 717, 170, 42, 43, 44, 700, 171, 701, 727, 45, 172, 46, 48, 49, 702, 50, 737, 51

Offset

1,3

Comments

The sequence starts with a(1) = 0 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction. This sequence is a permutation of the numbers >= 0.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..1208

Example

There are:
0 digit  between the 7 of "7" and the 7 of "70";
1 digit  between the 7 of "70" and the 7 of "71";
2 digits between the 7 of "71" and the 7 of "72";
3 digits between the 7 of "72" and the 7 of "17";
4 digits between the 7 of "17" and the 7 of "73";
5 digits between the 7 of "73" and the 7 of "74";
6 digits between the 7 of "74" and the 7 of "27";
7 digits between the 7 of "27" and the 7 of "37";
7 digits between the 7 of "37" and the 7 of "47";
0 digit  between the 7 of "47" and the 7 of "75";
7 digits between the 7 of "75" and the 7 of "76";
1 digit  between the 7 of "76" and the 7 of "78";
etc.
We see that the first column here is the succession of the digits of the sequence, as well as the size of each chunk of digits between two successive 7's.

Crossrefs

Cf. A303151 for the same idea with 1's as chunk's separators, A303157 with 2's, A303158 with 3's, A302943 with 4's, A303163 with 5's, A303164 with 6's, A303167 with 8's and A303171 with 9's.

Sequence in context: A370776 A273475 A278942 * A024649 A037335 A028429

Adjacent sequences: A303163 A303164 A303165 * A303167 A303168 A303169

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 19 2018

Status

approved