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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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5
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| R. E. Kutz, Two unusual sequences, Two-Year College Mathematics Journal, 12 (1981), 316-319.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| 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, R. J. Mathar, Mar 06 2010
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MAPLE
| f := proc(n, i, x) option remember ; if n = 0 then x; elif type(n, 'even') then procname(n/2, i+1, x) ; else procname((n-1)/2, i, x*ithprime(i)) ; end if; end proc:
A005940 := proc(n) f(n-1, 1, 1) ; end proc: # R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 06 2010
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MATHEMATICA
| 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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PROG
| (PARI) A005940(n) = { my(p=2, t=1); n--; until(!n\=2, n%2 & (t*=p) | p=nextprime(p+1)); t } [From M. F. Hasler (www.univ-ag.fr/~mhasler), Mar 07 2010]
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CROSSREFS
| Cf. A103969. Inverse is A005941.
Cf. A125106. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Mar 06 2010]
Sequence in context: A099004 A055170 A068384 * A005941 A075164 A023841
Adjacent sequences: A005937 A005938 A005939 * A005941 A005942 A005943
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2005
Sign in a formula switched and Maple program added - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 06 2010
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