

A078943


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).


3



1, 2, 4, 7, 3, 8, 14, 21, 13, 22, 12, 23, 11, 24, 10, 25, 9, 26, 44, 63, 43, 64, 42, 19
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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 nth step, so that we hit every positive integer exactly once?


LINKS

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


EXAMPLE

a(9)=13, so a(10) is either 139=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.
Sequence in context: A084332 A081145 A100707 * 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



