A078943 a(1)=1; a(n+1) is either a(n)-n or a(n)+n, where we choose the smallest positive integer that's not among the values a(1), ..., a(n).

1, 2, 4, 7, 3, 8, 14, 21, 13, 22, 12, 23, 11, 24, 10, 25, 9, 26, 44, 63, 43, 64, 42, 19

Offset: 1

Author

Leroy Quet, Dec 15 2002

Keywords

• nonn
• fini
• full

Comments

After a(24)=19, there are no more terms because a(24)-24 = -5 is not positive and a(24)+24 = 43 is equal to a(21).

If we only require that a(n+1) be either a(n)-n or a(n)+n, is there a sequence that contains every positive integer exactly once? I.e., can we take a walk on the positive integers starting at 1 and always moving (either left or right) a distance n on the n-th step so that we hit every positive integer exactly once?

A356080 is targeted to be such a sequence, but starting from 0. Its definition incorporates a limited look-ahead condition that is clearly a necessary condition for the sequence not to encounter a dead end (i.e., be finite) and is conjectured to be a sufficient condition. - Peter Munn, Feb 09 2023

Examples

			a(9)=13, so a(10) is either 13-9=4 or 13+9=22. But 4 is not available since it equals a(3), so a(10)=22.
		

Crossrefs

Consists of terms 1 through 25 of A063733.

Cf. A356080.

Extensions

Edited by Dean Hickerson, Dec 18 2002