A303163 Lexicographically earliest sequence of distinct terms such that the successive quantities of digits between two successive 5s are given by the succession of the sequence's digits itself.

0, 1, 2, 3, 4, 5, 50, 51, 6, 52, 7, 8, 53, 9, 10, 54, 11, 12, 56, 13, 14, 55, 16, 17, 15, 25, 18, 19, 20, 57, 21, 22, 58, 35, 23, 24, 26, 45, 27, 28, 29, 30, 59, 31, 32, 500, 65, 33, 34, 36, 37, 75, 85, 501, 38, 95, 39, 40, 505, 150, 502, 503, 41, 151, 42, 43, 152, 504, 153, 506, 44, 507, 46, 154, 47, 48, 515, 49, 60

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..1506

Example

There are:
0 digit  between the 5 of "5" and the 5 of "50";
1 digit  between the 5 of "50" and the 5 of "51";
2 digits between the 5 of "51" and the 5 of "52";
3 digits between the 5 of "52" and the 5 of "53";
4 digits between the 5 of "53" and the 5 of "54";
5 digits between the 5 of "54" and the 5 of "56";
5 digits between the 5 of "56" and the first 5 of "55";
0 digit  between the 5s of "5";
5 digits between the last 5 of "55" and the 5 of "15";
1 digit  between the 5 of "15" and the 5 of "25";
6 digits between the 5 of "25" and the 5 of "57";
5 digits between the 5 of "57" and the 5 of "58";
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 5s.

Crossrefs

Cf. A303151 for the same idea with 1s as chunk's separators, A303157 with 2s, A303158 with 3s, A302943 with 4s, A303164 with 6s, A303166 with 7s, A303167 with 8s and A303171 with 9s.

Sequence in context: A173574 A278940 A273470 * A024638 A037330 A062939

Adjacent sequences: A303160 A303161 A303162 * A303164 A303165 A303166

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 19 2018

Status

approved