A274689 A variation of A005228.

1, -1, 2, 6, 11, 8, 15, 10, 19, 13, 25, 21, 14, 30, 22, 39, 29, 20, 38, 27, 50, 37, 61, 49, 35, 63, 48, 32, 58, 41, 72, 54, 34, 67, 46, 82, 60, 100, 81, 57, 99, 76, 51, 94, 68, 112, 85, 56, 101, 73, 120, 90, 59, 111, 79, 132, 98, 65, 127, 92, 55, 119, 83, 149

Offset: 1

Author

Max Barrentine, Jul 02 2016

Keywords

• sign

Comments

This is the lexicographically earliest sequence such that the absolute value of its first differences (A274690) is minimal, and together with its first differences, contains every integer except zero at most once.

Each term is chosen so that |a(n+1) - a(n)| is minimal such that neither a(n+1) nor (a(n+1) - a(n)) has occurred previously in either this sequence or this sequence's first differences. If for a minimal term |k| k and -k are both available, choose the term that will minimize |a(n+1)|.

It appears that this sequence together with its first differences list every integer except zero.

Is -1 the only negative term?

Examples

			a(1) = 1; the next number with the lowest possible absolute value that has not occurred yet is -1, but since 1 + (-1) = 0 (which is not available because if a(n) = 0, then a(n+1) = a(n+1) - a(n)), -1 is not available. The next available terms are 2 and (-2). (-2) is chosen because |1 + 2| > |1 + (-2)|, so a(2) = 1 + (-2) = -1.
		

Crossrefs

Cf. A005228, A274690.