The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A078943

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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).
(history; published version)

#17 by Michel Marcus at Mon Aug 07 05:31:21 EDT 2023

STATUS

reviewed

approved

#16 by Joerg Arndt at Mon Aug 07 04:06:03 EDT 2023

STATUS

proposed

reviewed

#15 by Jon E. Schoenfield at Mon Aug 07 04:05:03 EDT 2023

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Mon Aug 07 04:04:59 EDT 2023

COMMENTS

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?

STATUS

approved

editing

#13 by Michael De Vlieger at Thu Feb 09 20:49:31 EST 2023

STATUS

proposed

approved

#12 by Peter Munn at Thu Feb 09 18:32:44 EST 2023

STATUS

editing

proposed

#11 by Peter Munn at Thu Feb 09 18:27:58 EST 2023

COMMENTS

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

CROSSREFS

Cf. A356080.

STATUS

approved

editing

#10 by Joerg Arndt at Mon Aug 15 09:02:03 EDT 2022

STATUS

editing

approved

#9 by Joerg Arndt at Mon Aug 15 09:01:33 EDT 2022

NAME

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

STATUS

approved

editing

#8 by N. J. A. Sloane at Tue Jun 24 01:08:34 EDT 2014

EXTENSIONS

Edited by _Dean Hickerson (dean.hickerson(AT)yahoo.com), _, Dec 18 2002

Discussion

Tue Jun 24

01:08

OEIS Server: https://oeis.org/edit/global/2238