A274687 Sequence and first differences (A274688) together list every integer except zero exactly once.

1, -1, 2, -3, 4, -4, 5, -6, 6, -7, 8, -9, 10, -10, 11, -12, 13, -14, 14, -15, 16, -16, 17, -18, 18, -19, 20, -21, 22, -22, 23, -24, 24, -25, 26, -26, 27, -28, 29, -30, 30, -31, 32, -33, 34, -34, 35, -36, 37, -38, 38, -39, 40, -40, 41, -42, 42, -43, 44, -45, 46

Offset: 1

Author

Max Barrentine, Jul 02 2016

Keywords

• sign

Comments

This is the lexicographically earliest sequence that together with its first differences (A274688) contains every integer except 0 exactly once.

Each term is chosen so that |a(n)| is minimal such that neither a(n) nor (a(n) - a(n-1)) has occurred previously in either this sequence or this sequence's first differences.

Examples

			a(1) = 1; the next number with the lowest possible absolute value that has not occurred yet is -1. -1 - (1) = -2, which also has not yet occurred, so a(2) = -1. The next available term is 2. 2 - (-1) = 3, which is also available, so a(3) = 2.
		

Crossrefs

Cf. A005228, A274688.