cp's OEIS Frontend

A366113 A fractal sequence. Pick any term t: exactly one of the t terms following t is larger than t.

%I A366113 #25 Oct 04 2023 12:38:30
%S A366113 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,1,2,1,3,1,7,1,2,1,3,1,2,8,1,2,1,3,1,
%T A366113 2,4,9,1,2,1,3,1,2,4,1,10,1,2,1,3,1,2,4,1,2,11,1,2,1,3,1,2,4,1,2,1,12,
%U A366113 1,2,1,3,1,2,4,1,2,1,5,13,1,2,1,3,1,2,4,1,2,1,5,1,14
%N A366113 A fractal sequence. Pick any term t: exactly one of the t terms following t is larger than t.
%C A366113 Starting with a(1) = 1, this is the lexicographically earliest sequence with this property.
%C A366113 This is how the sequence was built:
%C A366113 1) start with the Natural numbers and increase the gaps between them by one unit (first gap is zero):
%C A366113 S = 1,2,_,3,_,_,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8, …
%C A366113 2) fill the empty spaces with the successive _starting_ chunks of the sequence S _itself_:
%C A366113 S = 1,2,_,3,_,_,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, …
%C A366113 S = 1,2,1,3,_,_,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, …
%C A366113 S = 1,2,1,3,1,2,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, …
%C A366113 S = 1,2,1,3,1,2,4,1,2,1,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, …
%C A366113 S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, …
%C A366113 S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,1,2,1,3,1,7,_,_,_,_,_,_,8,_, …
%C A366113 S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,1,2,1,3,1,7,1,2,1,3,1,2,8,_, … Etc.
%H A366113 Neal Gersh Tolunsky, <a href="/A366113/b366113.txt">Table of n, a(n) for n = 1..10000</a>
%e A366113 One term out of 1 following a(1) = 1 is larger than 1: this is 2.
%e A366113 One term out of 2 following a(2) = 2 is larger than 2: this is 3.
%e A366113 One term out of 1 following a(3) = 1 is larger than 1: this is 2.
%e A366113 One term out of 3 following a(4) = 3 is larger than 3: this is 4.
%e A366113 One term out of 1 following a(5) = 1 is larger than 1: this is 2.
%e A366113 One term out of 2 following a(6) = 2 is larger than 2: this is 4.
%e A366113 One term out of 4 following a(7) = 4 is larger than 4: this is 5.
%e A366113 One term out of 1 following a(8) = 1 is larger than 1: this is 2.
%e A366113 One term out of 2 following a(9) = 2 is larger than 2: this is 5. Etc.
%t A366113 k=1;Nest[(k++;Join[#,#[[;;k-2]],{k}])&,{1},13] (* _Giorgos Kalogeropoulos_, Oct 03 2023 *)
%Y A366113 Cf. A342042.
%K A366113 nonn
%O A366113 1,2
%A A366113 _Eric Angelini_, Sep 29 2023
%E A366113 Data corrected by _Giorgos Kalogeropoulos_, Oct 03 2023