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The lexicographically earliest "Increasing Term Fractal Jump Sequence" that does not use the digit 0 in any terms.
2

%I #15 Dec 31 2022 10:49:54

%S 1,2,21,22,23,112,122,132,133,134,141,221,311,2112,2113,3111,21111,

%T 31113,31114,31124,31131,34111,41121,42111,43111,111121,111122,112111,

%U 112311,131111,211112,211113,1111311,1111312,3111311,3111312,4111131,4111132,4141111

%N The lexicographically earliest "Increasing Term Fractal Jump Sequence" that does not use the digit 0 in any terms.

%C The rules of an "Increasing Term Fractal Jump Sequence" are described in A105647.

%C The digit zero is omitted as it can create situations where the next term can require a 0 in the first digit.

%H Tyler Busby, <a href="/A359385/b359385.txt">Table of n, a(n) for n = 1..5000</a>

%e The sequence and the "kept" digits begin

%e 1, 2, 21, 22, 23, 112, 122, 132, 133, ...

%e ^ ^ ^ ^ ^ ^ ^ ^

%e 1 2 2 1 2 2 2 3

%Y Cf. A105647, A105395, A105396, A105397, A105398.

%K nonn,base

%O 1,2

%A _Tyler Busby_, Dec 29 2022