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A005941
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Inverse of the Doudna sequence A005940.
(Formerly M0510)
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11
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1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 17, 12, 33, 18, 11, 16, 65, 14, 129, 20, 19, 34, 257, 24, 13, 66, 15, 36, 513, 22, 1025, 32, 35, 130, 21, 28, 2049, 258, 67, 40, 4097, 38, 8193, 68, 23, 514, 16385, 48, 25, 26, 131, 132, 32769, 30, 37, 72, 259, 1026, 65537, 44, 131073, 2050, 39, 64
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OFFSET
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1,2
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COMMENTS
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a(2^k) = 2^k. - Robert G. Wilson v, Feb 22 2005
Fixed points: A029747. - Reinhard Zumkeller, Aug 23 2006
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REFERENCES
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J. H. Conway, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. J. Mathar, Table of n, a(n) for n=1,..,5000
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = h(g(n,1,1), 0) / 2 + 1 with h(n, m) = if n=0 then m else h(floor(n/2), 2*m + n mod 2) and g(n, i, x) = if n=1 then x else (if n mod prime(i) = 0 then g(n/prime(i), i, 2*x+1) else g(n, i+1, 2*x). - Reinhard Zumkeller, Aug 23 2006
a(n) = 1 + A156552(n). - Antti Karttunen, Jun 26 2014
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MAPLE
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(Maple code from R. J. Mathar, Mar 06 2010)
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:
A005941 := proc(n)
local k ;
for k from 1 do
if A005940(k) = n then
return k;
end if;
end do ;
end proc:
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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]}] ]]; t = Table[ f[n], {n, 10^5}]; Flatten[ Table[ Position[t, n, 1, 1], {n, 64}]] (* Robert G. Wilson v, Feb 22 2005 *)
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PROG
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(Scheme) (define (A005941 n) (+ 1 (A156552 n))) ;; Antti Karttunen, Jun 26 2014
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CROSSREFS
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Cf. A103969. Inverse of A005940. One more than A156552.
Sequence in context: A005940 A332815 A355405 * A355809 A269857 A269847
Adjacent sequences: A005938 A005939 A005940 * A005942 A005943 A005944
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Robert G. Wilson v, Feb 22 2005
a(61) inserted by R. J. Mathar, Mar 06 2010
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STATUS
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approved
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