A333399 The Zabriskie Point sequence: terms are blown up in honor of the final scene of Antonioni's movie (see the Comments section).

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, 35, 53, 36, 63, 37, 73, 38, 83, 39, 93, 40, 1104, 44, 45, 54, 46, 64, 47, 74

Offset: 1

Author

Eric Angelini and Carole Dubois, Mar 18 2020

Keywords

• base
• nonn

Comments

The sequence is started with a(1) = 1; the next term, a(2), must annihilate both a(1) and itself; this is done with a(1) = 1 and a(2) = 100; the disappearing rule is: "Two identical digits forming a pair explode and disappear instantly, even if they belong to two successive integers". We see with 1, 100 that the pair of 1's and the pair of 0's disappear, leaving nothing in the sequence. Said sequence is then extended with the smallest unused integer so far. This integer, if not annihilated by itself (like 11 would do, or 22, or 599500), must be blown up together with the one coming after it.

This sequence is both the lexicographically earliest sequence with this property and a permutation of the positive integers.

Examples

			a(1) = 1 and a(2) = 100 produce [1,100] which disappears (annihilation of the pair of 1's and of the pair of 0's);
a(3) = 2 as 2 is the smallest available integer not present so far in the sequence;
a(4) = 112 as 112 is the smallest available integer not present so far that annihilates both 2 and itself;
a(5) = 3 as 3 is the smallest available integer not present so far in the sequence;
a(6) = 113 as 113 is the smallest available integer not present so far that annihilates both 3 and itself; etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5000
• SeqFan mailing list, message from Eric Angelini on March 8, 2020
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A108988 (A twin's digits self-disappearing sequence).