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Fractal sequence which is left unchanged by interleaving it with the natural numbers, in such a way that each term k of the sequence is followed by the next k not-yet-seen natural numbers.
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%I #25 Nov 04 2023 14:00:17

%S 1,2,2,3,4,2,5,6,3,7,8,9,4,10,11,12,13,2,14,15,5,16,17,18,19,20,6,21,

%T 22,23,24,25,26,3,27,28,29,7,30,31,32,33,34,35,36,8,37,38,39,40,41,42,

%U 43,44,9,45,46,47,48,49,50,51,52,53,4,54

%N Fractal sequence which is left unchanged by interleaving it with the natural numbers, in such a way that each term k of the sequence is followed by the next k not-yet-seen natural numbers.

%C a(1) = 1. Each term a(n) = k is followed by the k smallest so-far-unseen natural numbers. Invented by _Eric Angelini_. Another way to say it (Angelini's formulation) is that when subjected to an erasure transformation, the k terms after a(n) = k are deleted, the original sequence is recovered; and if otherwise unconstrained, the natural numbers are introduced as soon as possible.

%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2023/05/a-simple-fractal-and-lynchean-sequence.html">A simple fractal (and lynchean) sequence</a>.

%K nonn,easy

%O 1,2

%A _Allan C. Wechsler_, May 20 2023