A363100 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.

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, 22, 23, 24, 25, 26, 3, 27, 28, 29, 7, 30, 31, 32, 33, 34, 35, 36, 8, 37, 38, 39, 40, 41, 42, 43, 44, 9, 45, 46, 47, 48, 49, 50, 51, 52, 53, 4, 54

Offset: 1

Author

Allan C. Wechsler, May 20 2023

Keywords

• nonn
• easy

Comments

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.

Links

• Eric Angelini, A simple fractal (and lynchean) sequence.