A306580 An irregular fractal sequence: underline all terms that share at least one digit with the preceding one. All underlined terms rebuild the starting sequence. (See the Comments section for more details.)

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 11, 1, 20, 2, 13, 3, 12, 30, 14, 4, 15, 5, 16, 6, 17, 7, 18, 8, 19, 9, 21, 10, 0, 22, 31, 11, 1, 23, 20, 2, 33, 13, 3, 24, 12, 34, 30, 25, 36, 27, 35, 26, 37, 28, 39, 40, 14, 4, 29, 38, 41, 15, 5, 32, 44, 50, 42, 51, 16, 6, 43, 52, 46, 53, 47, 17, 7, 45, 60, 48, 18, 8, 49, 19, 9, 54, 61, 21, 10, 0

Offset

1,3

Comments

The sequence S starts with a(1) = 0 and a(2) = 1. S is extended by duplicating the first term A among the not yet duplicated terms, under the condition that A shares at least one digit with the last term Z of the sequence. If A doesn't share any digit with Z, we then extend the sequence with the smallest integer X not yet present in S and not sharing a digit with Z.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..20002

Example

After S = 0, 1, ... we cannot extend S with 0 (first not yet duplicated term) because 0 doesn't share any digit with 1: S is then extended with 2 (because 2 is the smallest integer not yet present in S that doesn't share a digit with 1);
After S = 0, 1, 2, ... we still cannot extend S with 0: S is then extended with 3 (because 3 is the smallest integer not yet present in S that doesn't share a digit with 2);
After S = 0, 1, 2, 3, ... we still cannot extend S with 0: S is then extended with 4 (because 4 is the smallest integer not yet present in S that doesn't share a digit with 3);
[...]
After S = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... we must extend S with 0 as 0 shares a digit with 10;
After S = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, ... we cannot extend S with 1 (first not yet duplicated term) because 1 doesn't share any digit with 0: S is then extended with 11 (because 11 is the smallest integer not yet present in S that doesn't share a digit with 0);
After S = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 11, ... we must extend S with 1 as 1 shares a digit with 11;
After S = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 11, 1, ... we cannot extend S with 2 (next not yet duplicated term) because 2 doesn't share any digit with 1: S is then extended with 20 (because 20 is the smallest integer not yet present in S that doesn't share a digit with 1);
etc.

Crossrefs

Sequence in context: A210944 A259434 A329079 * A320486 A321801 A278946

Adjacent sequences: A306577 A306578 A306579 * A306581 A306582 A306583

Keyword

base,nonn,look

Author

Eric Angelini and Jean-Marc Falcoz, Feb 24 2019

Status

approved