

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.)


2



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
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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

JeanMarc 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 JeanMarc Falcoz, Feb 24 2019


STATUS

approved



