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A005941 Inverse of the Doudna sequence A005940.
(Formerly M0510)
11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(2^k) = 2^k. - _Robert G. Wilson v_, Feb 22 2005

Fixed points: A029747. - _Reinhard Zumkeller_, Aug 23 2006

REFERENCES

J. H. Conway, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

R. J. Mathar, Table of n, a(n) for n=1,..,5000

Index entries for sequences that are permutations of the natural numbers

FORMULA

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

MAPLE

(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:

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]}] ]]; t = Table[ f[n], {n, 10^5}]; Flatten[ Table[ Position[t, n, 1, 1], {n, 64}]] (* _Robert G. Wilson v_, Feb 22 2005 *)

PROG

(Scheme) (define (A005941 n) (+ 1 (A156552 n))) ;; _Antti Karttunen_, Jun 26 2014

CROSSREFS

Cf. A103969. Inverse of A005940. One more than A156552.

Sequence in context: A324106 A252753 A005940 * A269857 A269847 A245705

Adjacent sequences:  A005938 A005939 A005940 * A005942 A005943 A005944

KEYWORD

nonn

AUTHOR

_N. J. A. Sloane_

EXTENSIONS

More terms from _Robert G. Wilson v_, Feb 22 2005

a(61) inserted by _R. J. Mathar_, Mar 06 2010

STATUS

approved

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Last modified February 20 13:54 EST 2020. Contains 332078 sequences. (Running on oeis4.)