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Search: id:A078943
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| A078943 |
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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). |
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+0
2
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| 1, 2, 4, 7, 3, 8, 14, 21, 13, 22, 12, 23, 11, 24, 10, 25, 9, 26, 44, 63, 43, 64, 42, 19
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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?
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EXAMPLE
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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.
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CROSSREFS
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Consists of terms 1 through 25 of A063733.
Sequence in context: A084332 A081145 A100707 this_sequence A063733 A114375 A074958
Adjacent sequences: A078940 A078941 A078942 this_sequence A078944 A078945 A078946
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KEYWORD
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nonn,fini,full
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Dec 15 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 18 2002
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