A318452 Lexicographically first sequence of different positive terms starting with a(1) = 1, such that a(n+1) is obtained by subtracting or adding to a(n) a term already in the sequence. This term can be subtracted only once and added only once.

1, 2, 4, 3, 6, 10, 7, 5, 11, 16, 9, 18, 8, 15, 23, 12, 22, 13, 24, 19, 31, 25, 17, 30, 14, 28, 43, 20, 36, 21, 38, 26, 44, 27, 46, 32, 52, 33, 29, 50, 37, 59, 34, 57, 35, 60, 39, 63, 45, 71, 40, 67, 41, 69, 42, 72, 48, 77, 47, 78, 49, 81, 53, 86, 51, 85, 65, 100, 54, 90, 56, 93, 55, 94, 58, 96, 64, 104, 61, 102, 62, 105, 66

Offset

1,2

Comments

This sequence is a derangement of the positive integers.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Example

The sequence starts with 1,2,4,3,6,10,7,...
As all the terms of the sequence must be > 0, we cannot subtract 1 from term 1; thus a(2) is 1 (the last term) + the term a(1) = 1 + 1 = 2;
as we cannot add twice the same term, a(3) must be 2 (the last term) + a(2) = 2 + 2 = 4;
as the sequence must be the lexicographically first of its kind, and because all terms of the sequence must be different, we subtract the term a(1) = 1 from 4 (the last term) getting 3;
as we cannot subtract twice the same term, a(5) must be 3 (the last term) + the term a(4) = 3 + 3 = 6;
as the only available term for an addition to the last term a(5) is a(2) = 4, we have a(6) = 6 + 4 = 10;
as the sequence must be the lexicographically first of its kind, and because all terms of the sequence must be different, we subtract the term a(4) = 3 from 10 (the last term), getting 7;
etc.

Crossrefs

Sequence in context: A283961 A333029 A175498 * A083673 A327120 A131388

Adjacent sequences: A318449 A318450 A318451 * A318453 A318454 A318455

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Aug 26 2018

Status

approved