# [seqfan] Zabriskie point sequence

Éric Angelini bk263401 at skynet.be
Sun Mar 8 19:28:37 CET 2020

```Hello SeqFans,

The aim:
To detonate as fast as possible an emerging sequence.

Two identical digits forming a pair explode and disappear instantly, even if they belong to two successive integers [112 -> 2], [111 -> 1], [13,37 --> 1,7].
When all terms of S have exploded, we extend S with the smallest integer k not used before.
Example: after S = 1, 100 we extend S with k = a(3) = 2.
This k must be blown up immediately, together with the smallest available a(n+1) -- even if successive explosions are needed.
Example: to detonate 10, we can use 1101 as the chain reaction will be 10, 1101 -> 10,01 -> 11 -> ... and nothing is left.
S is the lexicographically earliest sequence of distinct positive integers keeping a trace of the successive detonations.

S = 1,100,2,112,3,113,4,114,5,115,6,116,7,117,8,118,9,119,10,1101,11,12,21,13,31,14,41,15,51,16,61,17,71,18,81,19,91,20,1102,22,23,32,24,42,25,52,26,62,27,72,28,82,29,92,30,1103,33,34,43,...

A108988 inspired the above idea.
And Antonioni: