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

1,2

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

Links

Table of n, a(n) for n=1..24.

Example

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.

Sequence in context: A081145 A100707 A302663 * A063733 A187089 A141330

Adjacent sequences: A078940 A078941 A078942 * A078944 A078945 A078946

Keyword

nonn,fini,full

Author

Leroy Quet, Dec 15 2002

Extensions

Edited by Dean Hickerson, Dec 18 2002

Status

approved