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Smallest positive integer such that for any n no substring (subsequence without internal skips) of length n is repeated unless it contains the number n or higher.
1

%I #14 Jun 04 2021 12:30:32

%S 1,1,2,1,2,2,1,3,1,2,3,1,2,4,1,2,3,2,1,3,2,1,4,1,2,3,3,1,2,4,2,1,3,3,

%T 1,3,1,3,2,2,2,3,1,3,3,2,1,4,2,1,3,4,1,2,3,4,1,2,4,1,3,1,4,1,2,4,2,2,

%U 3,2,2,3,3,2,2,4,1,2,4,3,1,2,4,3,2,1,4

%N Smallest positive integer such that for any n no substring (subsequence without internal skips) of length n is repeated unless it contains the number n or higher.

%H André Engels, <a href="/A329173/b329173.txt">Table of n, a(n) for n = 1..10000</a>

%e After 1,1,2,1,2, the next element is 2, because a 1 would repeat the length 3 substring 1,2,1. A 2 repeats the length 2 substring 2,2, but that's allowed because it contains a 2.

%K nonn

%O 1,3

%A _André Engels_, Nov 07 2019