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Search: id:A064389
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| A064389 |
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Variation (4) on Recaman's sequence (A005132): to get a(n), we first try to subtract n from a(n-1): a(n) = a(n-1)-n if positive and not already in the sequence; if not then we try to add n: a(n) = a(n-1)+n if not already in the sequence; if this fails we try to subtract n+1 from a(n-1), or to add n+1 to a(n-1), or to subtract n+2, or to add n+2, etc., until one of these produces a positive number not already in the sequence - this is a(n). |
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+0
7
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| 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 44, 19, 45, 72, 100, 71, 101, 70, 38, 5, 39, 4, 40, 77, 115, 76, 36, 78, 120, 163, 119, 74, 28, 75, 27, 79, 29, 80, 132, 185, 131, 186, 130, 73, 15, 81, 141, 202
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is the nicest of these variations. Is this a permutation of the natural numbers?
The number of steps before n appears is the inverse series, A078758. The height of n is in A126712.
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REFERENCES
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Suggested by J. C. Lagarias.
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LINKS
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Nick Hobson, Table of n, a(n) for n=1..10000
Nick Hobson, Python program for this sequence
Index entries for sequences related to Recaman's sequence
Index entries for sequences that are permutations of the natural numbers
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MAPLE
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h := array(1..100000); maxt := 100000; a := array(1..1000); a[1] := 1; h[1] := 1; for nx from 2 to 1000 do for i from 0 to 100 do t1 := a[nx-1]-nx-i; if t1>0 and h[t1] <> 1 then a[nx] := t1; if t1 < maxt then h[t1] := 1; fi; break; fi; t1 := a[nx-1]+nx+i; if h[t1] <> 1 then a[nx] := t1; if t1 < maxt then h[t1] := 1; fi; break; fi; od; od; evalm(a);
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CROSSREFS
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Cf. A005132, A046901, A064387, A064388. Agrees with A064387 for first 187 terms, then diverges.
Adjacent sequences: A064386 A064387 A064388 this_sequence A064390 A064391 A064392
Sequence in context: A005132 A064388 A064387 this_sequence A118201 A113880 A098141
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 28 2001
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