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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: A207801 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 November 21 16:08 EST 2017. Contains 295003 sequences.