Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 May 19 2020 19:15:28
%S 0,0,1,0,0,0,2,0,0,0,0,1,1,0,1,2,1,0,2,1,1,1,2,0,1,0,1,0,2,2,0,2,0,1,
%T 1,1,0,0,1,2,2,1,2,0,0,1,3,0,0,0,3,1,0,0,2,1,0,0,3,0,1,0,3,2,0,0,2,2,
%U 2,0,0,3,2,1,0,1,1,2,1,1,0,2,0,2,1,2,1
%N For any n > 0, let w be the least positive number such that the values (a(n+1-w), ..., a(n-1), e) do not appear continuously in (a(1), ..., a(n-1)) for some e in 0..w-1; a(n) is the least such e.
%C This sequence is an unbounded variant of A334941.
%C Will every finite sequence of nonnegative integers appear?
%H Rémy Sigrist, <a href="/A334944/a334944.png">Colored scatterplot of the ordinal transform of the first 1000000 terms</a>
%H Rémy Sigrist, <a href="/A334944/a334944.pl.txt">Perl program for A334944</a>
%e For n = 1:
%e - for w = 1: (0) did not appear,
%e - so a(1) = 0.
%e For n = 2:
%e - for w = 1: (0) appeared,
%e - for w = 2: (0, 0) did not appear,
%e - so a(2) = 0.
%e For n = 3:
%e - for w = 1: (0) appeared,
%e - for w = 2: (0, 0) appeared but (0, 1) did not,
%e - so a(3) = 1.
%o (Perl) See Links section.
%Y See A334941 and A334956 for similar sequences.
%K nonn
%O 1,7
%A _Rémy Sigrist_, May 17 2020