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Search: id:A005940
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| A005940 |
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The Doudna sequence: write n-1 in binary; power of p_k in a(n) is # of 1's that are followed by k-1 0's.
(Formerly M0509)
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+0
4
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| 1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 25, 18, 27, 16, 11, 14, 21, 20, 35, 30, 45, 24, 49, 50, 75, 36, 125, 54, 81, 32, 13, 22, 33, 28, 55, 42, 63, 40, 77, 70, 105, 60, 175, 90, 135, 48, 121, 98, 147, 100, 245, 150, 225, 72, 343, 250, 375, 108, 625, 162, 243, 64, 17, 26, 39
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A permutation of the natural numbers. - Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2005
Fixed points: A029747. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 23 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. E. Kutz, Two unusual sequences, Two-Year College Mathematics Journal, 12 (1981), 316-319.
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LINKS
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R. Zumkeller, Table = of n, a(n) for n = 1..1024
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = f(n-1, 1, 1) with f(n, i, x) = if n=0 then x = else (if n mod 2 = 0 then f(n/2, i+1, x) else f((n+1)/2, i, x*prime(i))). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 23 2006
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MATHEMATICA
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f[n_] := Block[{p = Partition[ Split[ Join[ IntegerDigits[n - 1, 2], {2}]], 2]}, Times @@ Flatten[ Table[q = Take[p, -i]; Prime[ Count[ Flatten[q], 0] + 1]^q[[1, 1]], {i, Length[p]}] ]]; Table[ f[n], {n, 67}] (from Robert G. Wilson v Feb 22 2005)
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CROSSREFS
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Cf. A103969. Inverse is A005941.
Adjacent sequences: A005937 A005938 A005939 this_sequence A005941 A005942 A005943
Sequence in context: A099004 A055170 A068384 this_sequence A005941 A075164 A023841
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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) and J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2005
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